Description
Book SynopsisThis 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 u
Table of Contents
Preface. Part I Basic Topics of Linear Continuous-Time Time-Invariant Dynamical Systems. Introduction. Classes of Systems. System Regimes. Transfer Function Matrix G(S). Part II Full Transfer Function Matrix F(S) and System Realization. Problem Statement. Nondegenerate Matrices. Definition of F(S). Determination of F(S). Full Block Diagram Algebra. Physical Meaning of F(S). System Matrix and Equivalence. Realizations of F(S). Part III Stability Study. Lyapunov Stability. Bounded Input Stability. Part IV Conclusion. Motivation for the Book. Summary of the Contributions. Future Teaching and Research. Part V Appendices. Appendix A: Notation. Appendix B: From Io System to Iso System. Appendix C: From ISO System to IO System. Appendix D: Relationships Among System Descriptions. Appendix E: Laplace Transforms and Dirac Impulses. Appendix F: Proof of Theorem 142. Appendix G: Example: F(S) of a MIMO System. Appendix H: Proof of Theorem 165. Appendix I: Proof for Example 167. Appendix J: Proof of Theorem 168. Appendix K: Proof of Theorem 176. Appendix L: Proof of Theorem 179. Appendix M: Proof of Theorem 183. Index.
