Contents Dedication Preface 0.1 On the state of the art 0.2 On the book 0.3 In gratitude Part 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 system 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 3.4 Desired regime 3.

5 Deviations and mathematical models 3.6 Stationary and nonstationary regimes 3.7 Equilibrium regime 4 Transfer function matrix G(s) Part II FULL TRANSFER FUNCTION MATRIX F(S) AND SYSTEM REALIZATION 5 Problem statement 6 Nondegenerate matrices 7 Definition of F(s) 7.1 Definition of F(s) in general 7.2 Definition of F(s) of the IO system 7.3 Definition of F(s) of the ISO system 7.4 Definition 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 series 9.4 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 12.3 Realizations of F(s) of IO systems 12.

4 Realizations of F(s) of ISO systems 12.5 Realizations of F(s) of IIO systems Part III STABILITY STUDY 13 Lyapunov stability 13.1 Lyapunov stability concept 13.2 Lyapunov stability definitions 13.3 Lyapunov method and theorems 13.4 Lyapunov stability conditions via F(s) 14 Bounded Input stability 14.1 BI stability and initial conditions 14.2 BI stability definitions 14.

3 BI stability conditions Part IV CONCLUSION 15 Motivation for the book 16 Summary of the contributions 17 Future teaching and research Part V Appendices A Notation A.0.4 Abbreviations A.0.5 Indexes A.0.6 Letters A.0.

7 Names A.0.8 Symbols and vectors A.0.9 Units B From IO system to ISO system C From ISO system to IO system D Relationships among system descriptions E Laplace transforms and Dirac impulses E.1 Laplace transforms E.2 Dirac impulses F Proof of Theorem 142 G Example: F(s) of a MIMO system H Proof of Theorem 165 I Proof for Example 167 J Proof of Theorem 168 K Proof of Theorem 176 L Proof of Theorem 179 M Proof of Theorem 183 Author Index Subject Index ;/P> 3.4 Desired regime 3.

5 Deviations and mathematical models 3.6 Stationary and nonstationary regimes 3.7 Equilibrium regime 4 Transfer function matrix G(s) Part II FULL TRANSFER FUNCTION MATRIX F(S) AND SYSTEM REALIZATION 5 Problem statement 6 Nondegenerate matrices 7 Definition of F(s) 7.1 Definition of F(s) in general 7.2 Definition of F(s) of the IO system 7.3 Definition of F(s) of the ISO system 7.4 Definition 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 series 9.4 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 12.3 Realizations of F(s) of IO systems 12.

4 Realizations of F(s) of ISO systems 12.5 Realizations of F(s) of IIO systems Part III STABILITY STUDY 13 Lyapunov stability 13.1 Lyapunov stability concept 13.2 Lyapunov stability definitions 13.3 Lyapunov method and theorems 13.4 Lyapunov stability conditions via F(s) 14 Bounded Input stability 14.1 BI stability and initial conditions 14.2 BI stability definitions 14.

3 BI stability conditions Part IV CONCLUSION 15 Motivation for the book 16 Summary of the contributions 17 Future teaching and research Part V Appendices A Notation A.0.4 Abbreviations A.0.5 Indexes A.0.6 Letters A.0.

7 Names A.0.8 Symbols and vectors A.0.9 Units B From IO system to ISO system C From ISO system to IO system D Relationships among system descriptions E Laplace transforms and Dirac impulses E.1 Laplace transforms E.2 Dirac impulses F Proof of Theorem 142 G Example: F(s) of a MIMO system H Proof of Theorem 165 I Proof for Example 167 J Proof of Theorem 168 K Proof of Theorem 176 L Proof of Theorem 179 M Proof of Theorem 183 Author Index Subject Index m 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 series 9.4 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 12.3 Realizations of F(s) of IO systems 12.4 Realizations of F(s) of ISO systems 12.5 Realizations of F(s) of IIO systems Part III STABILITY STUDY 13 Lyapunov stability 13.1 Lyapunov stability concept 13.

2 Lyapunov stability definitions 13.3 Lyapunov method and theorems 13.4 Lyapunov stability conditions via F(s) 14 Bounded Input stability 14.1 BI stability and initial conditions 14.2 BI stability definitions 14.3 BI stability conditions Part IV CONCLUSION 15 Motivation for the book 16 Summary of the contributions 17 Future teaching and research Part V Appendices A Notation A.0.4 Abbreviations A.

0.5 Indexes A.0.6 Letters A.0.7 Names A.0.8 Symbols and vectors A.

0.9 Units B From IO system to ISO system C From ISO system to IO system D Relationships among system descriptions E Laplace transforms and Dirac impulses E.1 Laplace transforms E.2 Dirac impulses F Proof of Theorem 142 G Example: F(s) of a MIMO system H Proof of Theorem 165 I Proof for Example 167 J Proof of Theorem 168 K Proof of Theorem 176 L Proof of Theorem 179 M Proof of Theorem 183 Author Index Subject Index izations of F(s) of ISO systems 12.5 Realizations of F(s) of IIO systems Part III STABILITY STUDY 13 Lyapunov stability 13.1 Lyapunov stability concept 13.2 Lyapunov stability definitions 13.3 Lyapunov method and theorems 13.

4 Lyapunov stability conditions via F(s) 14 Bounded Input stability 14.1 BI stability and initial conditions 14.2 BI stability definitions 14.3 BI stability conditions Part IV CONCLUSION 15 Motivation for the book 16 Summary of the contributions 17 Future teaching and research Part V Appendices A Notation A.0.4 Abbreviations A.0.5 Indexes A.

0.6 Letters A.0.7 Names A.0.8 Symbols and vectors A.0.9 Units B From IO system to ISO system C From ISO system to IO system D Relationships among system descriptions E Laplace transforms and Dirac impulses E.

1 Laplace transforms E.2 Dirac impulses F Proof of Theorem 142 G Example: F(s) of a MIMO system H Proof of Theorem 165 I Proof for Example 167 J Proof of Theorem 168 K Proof of Theorem 176 L Proof of Theorem 179 M Proof of Theorem 183 Author Index Subject Index lt;P> A Notation A.0.4 Abbreviations A.0.5 Indexes A.0.6 Letters A.

0.7 Names A.0.8 Symbols and vectors A.0.9 Units B From IO system to ISO system C From ISO system to IO system D Relationships among system descriptions E Laplace transforms and Dirac impulses E.1 Laplace transforms E.2 Dirac impulses F Proof of Theorem 142 G Example: F(s) of a MIMO system H Proof of Theorem 165 I Proof for Example 167 J Proof of Theorem 168 K Proof of Theorem 176 L Proof of Theorem 179 M Proof of Theorem 183 Author Index Subject In.