Chapter 1 System Model 1.1 Introduction 1.2 Models of Systems 1.2.1 Differential Equation 1.2.2 Transfer Function 1.2.3 The State-space Model 1.3 Transition from One Mathematical Modelto Another 1.3.1 From Differential Equation to Transfer Function for SISO Systems 1.3.2 From Transfer Function to Differential Equation for SISO Systems' 1.3.3 From G(s) to g(t) and Vice Versa 1.3.4 From State Equations to Transfer Function Matrix 1.3.5 From Transfer Function Matrix to State Equations for SISO Systems' 1.4 Summary Appendix: Three Power Generation Models Exercise
Chapter 2 Anear Transformation of State Vector 2.1 Linear Algebra 2.2 Transform to Diagonal Form and Jordan Form Exercise
Chapter 3 Solution of State Space Model 3.1 Introduction 3.2 Solution ofLTI State Equations 3.3 State TransferMatrix 3.3.1 Properties 3.3.2 Calculating the state transition matrix 3.4 Discretization 3.5 Solution of Discrete-Time Equation 3.6 Summary Exercise
Chapter 4 Stable Analysis 4.1 Introduction 4.2 Definition 4.3 Stability Criteria 4.3.1 Lyapunov's Second Method 4.3.2 State Dynamics Stability Criteria for Continuous Linear Systems 4.3.3 State Dynamics Stability Criteria for Discrete Systems 4.4 Summary Exercise
Chapter 5 Controllability and Observability 5.1 Introduction 5.2 Definition 5.2.1 Controllability 5.2.2 Observability 5.3 Criteria 5.3.1 Controllable Criteria 5.3.2 Controllable Examples 5.3.3 Observable Criteria 5.3.4 Observable Examples 5.4 Duality System 5.4.1 Definition 5.4.2 Properties of Duality Systems 5.5 Canonical Form 5.5.1 Controllability Canonical Form of Single-Input Systems 5.5.2 Observability Canonical Form of Single-Output Systems 5.5.3 Example 5.5.4 Observability and Controllability Canonical Form ofMulti-Input Multi-Output Systems 5.6 System Decomposition 5.6.1 Controllability Decomposition 5.6.2 Observability Decomposition 5.6.3 Controllability and Observability Decomposition 5.6.4 Minimum Realization 5.7 Summary Exercise ……
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