Linear continuous-time systems

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. Content: Cover Half Title Title Page Copyright Page Dedication Table of Contents List of Figures Preface I: BASIC TOPICS OF LINEAR CONTINUOUS-TIME TIME-INVARIANT DYNAMICAL SYSTEMS 1: Introduction 1.1 Time 1.2 Time, physical principles, and systems 1.3 Time and system dynamics 1.4 Systems and complex domain 1.5 Notational preliminaries 2: Classes of systems 2.1 IO systems 2.2 ISO systems 2.3 IIO systems 3: System Regimes 3.1 System regime meaning 3.2 System regimes and initial conditions 3.3 Forced and free regimes 3.3.1 Introduction 3.7.3 ISO systems3.7.4 IIO systems 4: Transfer function matrix G(s) II: FULL TRANSFER FUNCTION MATRIX F(S) AND SYSTEM REALIZATION 5: Problem statement 6: Nondegenerate matrices 7: Defnition of F(s) 7.1 Defnition of F(s) in general 7.2 Defnition of F(s) of the IO system 7.3 Defnition of F(s) of the ISO system 7.4 Defnition of F(s) of the IIO system 8: Determination of F(s) 8.1 F(s) of the IO system 8.2 F(s) of the ISO system 8.3 F(s) of the IIO system 8.4 Conclusion: Common general form of F(s) 9: Full block diagram algebra 9.1 Introduction 9.2 Parallel connection 9.3 Connection in series9.4 Feedback connection 10: Physical meaning of F(s) 10.1 The IO system 10.2 The ISO system 10.3 The IIO system 11: System matrix and equivalence 11.1 System matrix of the IO system 11.2 System matrix of the ISO System 11.3 System matrix of the IIO system 12: Realizations of F(s) 12.1 Dynamical and least dimension of a system 12.2 On realization and minimal realization 12.2.1 Minimal realization of the transfer function matrix 12.2.2 Realization and minimal realization of the full transfer function matrix and the system 12.3 Realizations of F(s) of IO systems12.4 Realizations of F(s) of ISO systems 12.5 Realizations of F(s) of IIO systems III: STABILITY STUDY 13: Lyapunov stability 13.1 Lyapunov stability concept 13.2 Lyapunov stability definitions 13.2.1 IO systems 13.2.2 ISO systems 13.2.3 IIO systems 13.3 Lyapunov method and theorems 13.3.1 Outline of Lyapunov's original theory 13.3.2 Lyapunov method, theorems and methodology for the linear systems 13.3.3 Lyapunov theorem for the IO systems 13.3.4 Lyapunov theorem for the ISO systems 13.3.5 Lyapunov theorem for the IIO systems "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."--Provided by publisher "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. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the system full transfer function matrix F(s). The text also 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"-- Provided by publisher