Linear continuous time systems 1st Edition by Lyubomir T Gruyitch ISBN 1138039535 9781138039537
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ISBN 10: 1138039535
ISBN 13: 9781138039537
Author: Lyubomir T Gruyitch
Linear continuous time systems 1st Table of contents:
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
3.3.2 The temporal domain descriptions. The independent variable is time t∈T0t in T_0
3.3.3 The complex domain system descriptions. The independent variable is the complex variable s∈Cs in mathbb{C}
3.3.4 Basic problem
3.4 Desired regime
3.4.1 Introduction
3.4.2 IO systems
3.4.3 ISO systems
3.4.4 IIO systems
3.5 Deviations and mathematical models
3.5.1 Introduction
3.5.2 IO systems
3.5.3 ISO systems
3.5.4 IIO systems
3.6 Stationary and nonstationary regimes
3.6.1 Introduction
3.6.2 IO systems
3.6.3 ISO systems
3.6.4 IIO systems
3.7 Equilibrium regime
3.7.1 Introduction
3.7.2 IO systems
3.7.3 ISO systems
3.7.4 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. 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
12.2.1 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 systems
12.4 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
13.4 Lyapunov stability conditions via F(s)
13.4.1 Generating theorem
13.4.2 IO systems
13.4.3 ISO systems
13.4.4 IIO systems
14. Bounded Input stability
14.1 BI stability and initial conditions
14.2 BI stability definitions
14.2.1 IO systems
14.2.2 ISO systems
14.2.3 IIO systems
14.3 BI stability conditions
14.3.1 IO systems
14.3.2 ISO systems
14.3.3 IIO systems
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