By: Lyubomir T. Gruyitch
Subjects: Engineering - Chemical, Engineering - Electrical, Engineering - General, Engineering - Mechanical, Mathematics, Physics

Trackability and Tracking of General Linear Systems

1st Edition

Lyubomir T. Gruyitch

CRC Press 
November 2, 2018 

Reference - 378 Pages - 13 B/W Illustrations 
ISBN 9781138353374 - CAT# K395516

Summary

Trackability and Tracking of General Linear Systems deals with five classes of the systems, three of which are new, begins with the definition of time together with a brief description of its crucial properties and with the principles of the physical uniqueness and continuity of physical variables. They are essential for the natural tracking control synthesis. The book presents further new results on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the completion of the trackability and tracking concepts together with the proofs of the trackability and tracking criteria, as well as the natural tracking control synthesis for all five classes of the systems.

Features

• Crucially broadens the state space concept and the complex domain fundamentals of the dynamical systems to the control systems.

• Addresses the knowledge and ability necessary to study and design control systems that will satisfy the fundamental control goal.

• Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems.

• Upgrades, completes and essentially generalizes the control theory beyond the existing boundaries.

• Provides information necessary to create and teach advanced inherently upgraded control courses.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Chemical, Engineering - Electrical, Engineering - General, Engineering - Mechanical, Mathematics, Physics

Observability and Controllability of General Linear Systems

1st Edition

Lyubomir T. Gruyitch

CRC Press 
November 2, 2018 
Reference - 335 Pages - 1 B/W Illustrations 
ISBN 9781138353152 - CAT# K395488

Summary

Observability and Controllability of General Linear Systems treats five different families of the linear systems, three of which are new. The book begins with the definition of time together with a brief description of its crucial properties. It presents further new results on matrices, on polynomial matrices, on matrix polynomials, on rational matrices, and on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the proofs of the new necessary and sufficient observability and controllability conditions for all five classes of the studied systems.

Features

• Generalizes the state space concept and the complex domain fundamentals of the control systems unknown in previously published books by other authors.

• Addresses the knowledge and ability necessary to overcome the crucial lacunae of the existing control theory and drawbacks of its applications.

• Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems.

• Upgrades, completes and broadens the control theory related to the classical self-contained control concepts: observability and controllability.

• Provides information necessary to create and teach advanced inherently upgraded control courses.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Chemical, Engineering - Electrical, Engineering - Mechanical, Mathematics

Linear Discrete-Time Systems

Zoran M. Buchevats, Lyubomir T. Gruyitch

November 8, 2017 by CRC Press 
Reference - 454 Pages 
ISBN 9781138039599 - CAT# K32971

https://www.crcpress.com/Linear-Discrete-Time-Systems/Buchevats-Gruyitch/p/book/9781138039599 

Features

• Discovers the existence of the system full transfer function matrix F(z) and defines and determines it for IO, ISO, and IIO systems.
• Establishes the full block diagram technique and the full system matrix P(z), both based on the use of F(z).
• Introduces new dynamical system and control tools, which are not available in existing texts.
• Explores the concept and definition of the IO systems and IIO systems state, and uses it in the stability study.

Summary

This book covers crucial lacunae of the linear discrete-time time-invariant dynamical systems and introduces the reader to their treatment, while functioning under real, natural conditions, in forced regimes with arbitrary initial conditions. It provides novel theoretical tools necessary for the analysis and design of the systems operating in stated conditions. The text completely covers two well-known systems, IO and ISO, along with a new system, IIO. It discovers the concept of the full transfer function matrix F(z) in the z-complex domain, which incorporates the Z-transform of the system, input and another variable, vectors, all with arbitrary initial conditions. Consequently, it addresses the full system matrix P(z) and the full block diagram technique based on the use of F(z), which incorporates the Z-transform of the system, input and another variable, vectors, all with arbitrary initial conditions. The book explores the direct relationship between the system full transfer function matrix F(z) and the Lyapunov stability concept, definitions, and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the linear discrete-time time-invariant system, for short systems.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Chemical, Engineering - Electrical, Engineering - General, Engineering - Mechanical, Mathematics

Linear Continuous-Time Systems

Lyubomir T. Gruyitch

May 29, 2017 Forthcoming by CRC Press 
Reference - 469 Pages 
ISBN 9781138039506 - CAT# K32969

Features

• Discovers the existence of the system full transfer function matrix F(s) and defines and determines it for IO, ISO and IIO systems (the new class of the systems introduced in the book).
• Establishes the full block diagram technique and the full system matrix P(s) both based on the use of F(s).
• Introduces new dynamical system and control tools, which are not available in existing texts.
• Explores the concept and definition of the IO systems and of the IIO systems state and uses it in the stability study.
• Provides the understanding, knowledge, and capability to analyze and design all three classes of the systems.

Summary

This book aims to help the reader understand the linear continuous-time time-invariant dynamical systems theory and its importance for systems analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text completely covers IO, ISO and IIO systems. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the also newly introduced system full transfer function matrix F(s). The text establishes the full block diagram technique based on the use of F(s), which incorporates the Laplace transform of the input vector and the vector of all initial conditions. It explores the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the of the linear continuous-time time-invariant systems, for short systems.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Chemical, Engineering - Electrical, Engineering - General, Engineering - Mechanical, Mathematics

Nonlinear Systems Tracking

Lyubomir T. Gruyitch

January 2, 2016 by CRC Press 
Reference - 478 Pages - 16 B/W Illustrations 
ISBN 9781498753258 - CAT# K27341

Features

• Covers a very large class of time-varying nonlinear systems that incorporate the any-order input-output systems and those determined by the classical state-space description
• Presents new theories and concepts that begin by defining new system and control properties and end with the criteria or with the conditions on the system
• Solves the problem of achieving the tracking control task whatever the physical (biological, chemical, economical, electrical, electromechanical, mechanical, or social) nature of the plant
• Addresses the dynamical and control problems caused by the complexity of the system
• Uses the new simple vector and matrix notation analogous to the scalar notation

Summary

Tracking is the goal of control of any object, plant, process, or vehicle. From vehicles and missiles to power plants, tracking is essential to guarantee high-quality behavior.

Nonlinear Systems Tracking establishes the tracking theory, trackability theory, and tracking control synthesis for time-varying nonlinear plants and their control systems as parts of control theory. Treating general dynamical and control systems, including subclasses of input-output and state-space nonlinear systems, the book:

• Describes the crucial tracking control concepts that comprise effective tracking control algorithms
• Defines the main tracking and trackability properties involved, identifying properties both perfect and imperfect
• Details the corresponding conditions needed for the controlled plant to exhibit each property
• Discusses various algorithms for tracking control synthesis, attacking the tracking control synthesis problems themselves
• Depicts the effective synthesis of the tracking control, under the action of which, the plant behavior satisfies all the imposed tracking requirements resulting from its purpose

With clarity and precision, Nonlinear Systems Tracking provides original coverage, presenting discovery and proofs of new tracking criteria and control algorithms. Thus, the book creates new directions for research in control theory, enabling fruitful new control engineering applications.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Chemical, Engineering - Electrical, Engineering - General, Engineering - Mechanical, Mathematics

Nonlinear Systems Tracking

Lyubomir T. Gruyitch

January 2, 2016 by CRC Press 
Reference - 478 Pages - 16 B/W Illustrations 
ISBN 9781498753258 - CAT# K27341

https://www.crcpress.com/Nonlinear-Systems-Tracking/Gruyitch/9781498753258

Features

• Covers a very large class of time-varying nonlinear systems that incorporate the any-order input-output systems and those determined by the classical state-space description
• Presents new theories and concepts that begin by defining new system and control properties and end with the criteria or with the conditions on the system
• Solves the problem of achieving the tracking control task whatever the physical (biological, chemical, economical, electrical, electromechanical, mechanical, or social) nature of the plant
• Addresses the dynamical and control problems caused by the complexity of the system
• Uses the new simple vector and matrix notation analogous to the scalar notation

Summary

Tracking is the goal of control of any object, plant, process, or vehicle. From vehicles and missiles to power plants, tracking is essential to guarantee high-quality behavior.

Nonlinear Systems Tracking establishes the tracking theory, trackability theory, and tracking control synthesis for time-varying nonlinear plants and their control systems as parts of control theory. Treating general dynamical and control systems, including subclasses of input-output and state-space nonlinear systems, the book:

• Describes the crucial tracking control concepts that comprise effective tracking control algorithms
• Defines the main tracking and trackability properties involved, identifying properties both perfect and imperfect
• Details the corresponding conditions needed for the controlled plant to exhibit each property
• Discusses various algorithms for tracking control synthesis, attacking the tracking control synthesis problems themselves
• Depicts the effective synthesis of the tracking control, under the action of which, the plant behavior satisfies all the imposed tracking requirements resulting from its purpose

With clarity and precision, Nonlinear Systems Tracking provides original coverage, presenting discovery and proofs of new tracking criteria and control algorithms. Thus, the book creates new directions for research in control theory, enabling fruitful new control engineering applications.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Electrical, Engineering - Mechanical, Mathematics, Physics

GALILEAN–NEWTONEAN REBUTTAL TO

EINSTEIN’S RELATIVITY THEORY
Lyubomir T. Gruyitch, Serbia

ISBN-13: 978-1-907343-41-4; 390 pages, hardback, February 2015; £80.00/$125.00

http://www.cisp-publishing.com/acatalog/info_124.html 

Galilean-Newtonean physics is the basis for the presented in-debt study of Einstein`s works. Rigorous, exact, proofs of the EINSTEIN’S RELATIVITY full physical failure and mathematical sever restrictions on the validity of Einstein`s formulae exclusively under Einstein`s physically meaningless and mathematically unjustifiable assumptions The book discovers a number of the inconsistences, mistakes and paradoxes of Einstein`s relativity theory. The book presents the proofs that Einstein`s claims (lifted to the level of uncontested postulates) on the relativity of time itself, on the existence of several times and the time speeds, on the time dependence on space (frames), on the invariance of the light speed are wrong and physically meaningless. The book discovers Einstein`s tacit assumptions accepted a priory, which form the basis for all his mathematical results. The book explains and shows that all the assumptions are inacceptable, which makes all his mathematical results formally valid only under such assumptions and that his theory represents from the formal mathematical view point exclusively a singular case.

Order on line at:  www.cisp-publishing.com/acatalog/info_124.html

By: Lyubomir T. Gruyitch
Subjects: Engineering - Electrical, Engineering - General, Engineering - Mechanical, Mathematics, Physics

Time and Consistent Relativity
Physical and Mathematical Fundamentals

Lyubomir T. Gruyitch, DSc

http://www.appleacademicpress.com/title.php?id=9781771881111

In production
Pub Date: April, 2015
Hardback Price: $179.95 US | £114.00
Hard ISBN: 9781771881111
Pages: Approx 599pp+index
Binding Type: hardback

Time and Consistent Relativity: Physical and Mathematical Fundamentals establishes a new and original theory of time relativity, which is fully consistent. It explains why Einstein`s theory of time relativity is physically meaningless and mathematically based on tacit inacceptable assumptions, and why it represents the singular case from the mathematical point of view. The consistent relativity theory established in the book represents an exit from the situation created by Einstein`s theory of time relativity.

This original book presents novel results on time and its relativity that constitute the consistent relativity theory. The results are free of mistakes, inconsistencies, and paradoxes of Einstein`s time relativity theory. The author’s original discoveries and results constitute the new physical and mathematical fundamentals on time and its relativity. The book presentation is concise, clear, and self-contained. It covers the phenomenon of time and its properties and results in a definition and characterization of time. It enables the great variety of new mathematical results presented in the form of theorems and their corollaries and specifies the necessary and sufficient conditions for the corresponding statements to hold. The proofs are rigorous.

This book:

• explains the physical nature of time
• presents the definition and characterization of time
• explains the physical sense of time relativity
• rejects Einstein’s time relativity theory as the general one
• proves that Einstein’s time relativity theory represents a singular case valid under tacit, physically meaningless and mathematically inacceptable, assumptions
• generalizes and extends the Galilean-Newtonian meaning of time and its relativity
• introduces various new classes of mathematical transformations related to temporal, spatial, and velocity coordinates and proves the necessary and sufficient conditions for their validity
• discovers a great specter of new results on the time uniqueness, relativity, temporal speed
• discovers and proves a great specter of new results on the velocity and its transformations
• discovers and proves a great specter of new results on the light speed and its invariance and non-invariance
• discovers and proves the relationship of the light speed and the upper limiting speed
• opens new directions for further research in physics and mathematical physics.

CONTENTS:
Preface
Introduction
PART I. TIME
1. Interpretations of Time
1.1 Introductory comment
1.2 Time as a topic
1.3 Arts and time
1.4 Biology and time
1.5 Economics and time
1.6 Human and time
1.7 Information and time
1.8 Mathematics and time
1.9 Philosophy and time
1.10 Physics and time
1.11 Psychology and time
1.12 Religion and time
1.13 Works on time in general
1.14 Works on time
2. Newton and Einstein on Time
2.1 Newton's explanation of time
2.2 Einstein's interpretation of time
2.3 Einstein's versus Newton's explanation
3. Nature and Properties of Time
3.1 Quantities, dimensions and units
3.2 Definition and properties of time 
3.3 Time scales, units and interval mappings
3.4 Physical variables and spaces
3.5 Physical constituents of the existence
3.6 Time, space and events. Simultaneity
3.7 Time, velocity and light velocity
3.8 Clock principles
3.9 Time and movement
3.10 Human and time
4. New Fundamentals
4.1 Physical variables, time and new principles
4.2 Modeling and relativity principles
4.3 Time, principles and dynamical systems
4.4 New fundamental theorems

PART II. TIME FIELDS AND RELATIVITY
5. Time Fields and Transformations
5.1 Time field: definition and properties
5.2 Time fields. Generic transformations
5.3 Compatibility. Consistency
5.4 Basic mathematical problem
5.5 General, special and singular case
6. Why not Einstein`s Relativity Theory?
6.1 Einstein's condition and transformations
6.2 Time Fields and Lorentz transformations
6.3 Failure of Einstein`s Relativity Theory
6.4 Inapplicability of Lorentz transformations
6.5 Paradoxes of Lorentz transformations
6.6 Einstein`s paradoxes, mistakes and absurd
6.7 Concluding rebuttals to Einstein`s postulates
6.8 Conclusion on Einstein's Theory
7. Non-Einsteinean Approaches to Relativity
7.1 Galilean - Newtonean approach
7.2 Dynamical systems approach to relativity
7.3 Generalized Galilean - Newtonean approach
7.4 Guideline
8. Conclusion on Time and Time Fields

PART III. PARTIALLY COMPATIBLE BUT CONSISTENT (PCC) RELATIVITY THEORY (RT)
9. Partial Compatibility
9.1 Origin of partial compatibility
9.2 Time-invariant nonuniformity
9.3 Time-invariant uniformity
10. Light Speed of the Arbitrary Point
10.1 General nonuniformity
10.2 Nonuniformity
10.3 Weak nonuniformity
10.4 Uniformity: general through special
10.5 Weak uniformity results
10.6 Relative uniformity results
11. Any Speed of the Arbitrary Point
11.1 General spatial uniformity
11.2 General complete uniformity
12. Conclusion on PCC Relativity Theory

PART IV. COMPATIBLE AND CONSISTENT (CC) RELATIVITY THEORY
13. Colinear Motions: Transformations
13.1 Importance. Time-invariance
13.2 Nonuniformity: general
13.3 Nonuniformity: ordinary
13.4 Nonuniformity: weak
13.5 General uniformity
13.6 Uniformity
13.7 Special uniformity
13.8 General weak uniformity
13.9 Weak uniformity
13.10 Special weak uniformity
13.11 General relative uniformity
13.12 Relative uniformity
13.13 Special relative uniformity
13.14 Conclusion on colinear motions
14. Noncolinear Motions: Transformations
14.1 Generic forms
14.2 General nonuniformity
14.3 General uniformity
14.4 General weak uniformity
14.5 General relative uniformity
14.6 Conclusion on noncolinear motions
15. Conclusion on CC Relativity Theory

PART V. GENERAL CONCLUSION
PART VI. SUBSIDIARY PARTS
16. Bibliography
17. Notational Details
18. Appendices: Proofs
19. Indexes

By: Lyubomir T. Gruyitch
Subjects: Engineering - Electrical, Engineering - Mechanical, Mathematics

Tracking Control of Linear Systems

CRC Press, Taylor & Francis Group, Boca Raton, FL, USA, 2013

ISBN: 978-1-4665-8751-9

http://www.crcpress.com/product/isbn/9781466587519

Features

• Introduces the full transfer function matrix, which is a crucial complex domain characteristic of linear dynamical and control systems that can be used under arbitrary inputs and initial conditions
• Establishes the new fundamentals of the complex domain theory of linear dynamic and control systems
• Shows how the full transfer function matrix enables you to synthesize control of linear systems to work more effectively in real environments
• Discusses tracking and trackability fundamentals and their significance for control synthesis
• Presents novel, sophisticated approaches and methods for tracking control design
• Includes theorem proofs in the appendices

Summary

The primary purpose of control is to force desired behavior in an unpredictable environment, under the actions of unknown, possibly unmeasurable disturbances and unpredictable, and therefore probably nonzero, initial conditions. This means that tracking and tracking control synthesis are fundamental control issues. Surprisingly, however, tracking theory has not been well developed, and stability theory has dominated. Tracking Control of Linear Systems presents the fundamentals of tracking theory for control systems. The book introduces the full transfer function matrix F(s), which substantially changes the theory of linear dynamical and control systems and enables a novel synthesis of tracking control that works more effectively in real environments.

An Introduction to the New Fundamentals of the Theory of Linear Control Systems

The book begins by re-examining classic linear control systems theory. It then defines and determines the system full (complete) transfer function matrix F(s) for two classes of systems: input-output (IO) control systems and input-state-output (ISO) control systems. The book also discusses the fundamentals of tracking and trackability. It presents new Lyapunov tracking control algorithms and natural tracking control (NTC) algorithms, which ensure the quality of the tracking under arbitrary disturbances and initial conditions. This natural tracking control is robust, adaptable, and simple to implement.

Advances in Linear Control Systems Theory: Tracking and Trackability

This book familiarizes readers with novel, sophisticated approaches and methods for tracking control design in real conditions. Contributing to the advancement of linear control systems theory, this work opens new directions for research in time-invariant continuous-time linear control systems. It builds on previous works in the field, extending treatment of the system transfer functions, stability issues, the plant–control relationship, and control synthesis.

By: Lyubomir T. Gruyitch
Subjects: Engineering - Electrical, Engineering - Mechanical, Mathematics

ADVANCES IN THE LINEAR DYNAMIC SYSTEMS THEORY

Lyubomir T. Gruyitch

www.llumina.com/store/advancesinlineardynamics.htm

Llumina Press, 2013, www.llumina.com

ABSTRACT

The discovery of the full transfer function matrix F(s) of the linear dynamic system eliminates the deep and essential lacuna of their existing theory. It describes in the complex domain how the system simultaneously transmits and transfers both the action of the input vector and the influence of all initial conditions on the system output behavior. It has exactly the same properties as the classical system transfer function matrix G(s) that is valid only under all zero initial conditions. The full transfer function matrix is determined (together with all its submatrices) for the three classes of the systems, one of which is newly discovered.

The full transfer function matrix F(s) is the basis for the new, full (complete), block diagram system technique. It is established in this book. It essentially broadens the use and application of the classical block diagram technique that holds for zero initial conditions by its definition. The complete block diagram technique, being defined and developed for arbitrary initial conditions, fully overcomes the severe restriction of the classical block diagram technique.

Since Lyapunov stability properties are defined for nonzero initial conditions then their tests should be carried out by using F(s) because the use of G(s) can give the result opposite to the correct one, i.e. the result obtained via G(s) can be that the system is stable in spite it is unstable. The test via F(s) overcomes this problem.

BIBO stability was defined for zero initial conditions in order to test it effectively by using G(s). Initial conditions are almost always different from zero. Allowing non-zero initial conditions various new stability properties under bounded-input and for bounded arbitrary initial conditions are discovered and defined in this book. Their tests should be carried out by using F(s). G(s) is inapplicable.

For both Lyapunov stability properties and bounded-input and nonzero bounded initial conditions the new stability criteria proved in the book are in terms of F(s).

The book establishes the new system fundamental in the complex domain. It is inherent for the system stabilization and/or optimization. The discovers and the contributions of the book should essentially complete the university course in linear both control systems and dynamical systems. They open new avenues for research.

The book is equally significant and useful for lecturers, students, researchers as for linear dynamic system designers, control and system engineers.