目录:Chapter1 State Space Description
1.1 Definition of State Space
1.1.2 Definitions
1.1.3 State Space Description
1.1.4 Transfer Function Matrix
1.2 Obtaining State Space Description from I/O Description
1.2.1 Obtaining State Space Description from Differential Equation
1.2.2 Obtaining State Space Description from Transfer Function
1.2.3 Obtaining State Space Description from Block Diagram
1.3 Obtaining Transfer Function Matrix from State Space Description
1.4 Description of Composite Systems
1.4.1 Basic Connection of Composite Systems
1.4.2 Description of the Series Composite Systems
1.4.3 Description of the Parallel Composite Systems
1.4.4 Description of the Feedback Composite Systems
1.5 State Transformation of the LTI system
1.5.1 Eigenvalue and Eigenvector
1.5.2 State Transformation
1.5.3 Invariance Properties of the State Transformation
1.5.4 Obtaining the Diagonal Canonical Form by State Transformation
1.5.5 Obtaining the Jordan Canonical Form by State Transformation
Problems
Chapter2 Time Response of the LTI System
2.1 Time Response of the LTI Homogeneous System
2.2 State Transition Matrix
2.2.1 Definition
2.2.2 Properties of the State Transition Matrix
2.3 Calculation of the Matrix Exponential Function
2.3.1 Direct Method
2.3.2 Laplace Transform Method
2.3.3 Similarity Transformation Method
2.3.4 Cayley—Hamilton Theorem Method
2.4 Time Response of the LTI System
Problems
Chapter3 Stability of the control System
3.1 The Basics of Stability Theory in Mathematics
3.2.1 Equilibrium Point
3.2.2 Concepts of Lyapunov Stability
3.3 Lyapunov Stability Theory
3.3.1 Lyapunov First Method
3.3.2 Lyapunov Second Method
3.4 Application of Lyapunov 2nd Method to the LTI System
3.5 Construction of Lyapunov Function to the
Nonlinear System
Chapter4 Controllability and Observability
4.1 Controllability of The LTI System
4.1.1 Controllability
4.1.2 Criteria of Controllability
4.2 Observability of The LTI System
4.2.1 Observability
4.2.2 Criteria of Observability
4.3 Duality
4.4 Obtaining the Controllable and Observable Canonical Form by State
Transformation
4.4.1 Obtaining the Controllable Canonical Form by State Transformation
4.4.2 Obtaining the Observable Canonical Form by State Transformation
4.5 Canonical Decomposition of the LTI System
4.5.1 Controllable Canonical Decomposition
4.5.2 Observable Canonical Decomposition
4.5.3 Canonical Decomposition
4.6 Minimal Realization of the LTI System
4.6.1 Realization Problem
4.6.2 Realization of SISO System
4.6.3 Realization of MIMO System
4.6.4 Minimal Realization
Problems
Chapter5 Synthesis of the LTI System
5.1 State Feedback Control of the LTI System
5.1.1 State Feedback
5.1.2 Controllability and Observability of the Closed—Loop System
5.1.3 Poles Placement by State Feedback Control
5.1.4 Zeros of the Closed—Loop System
5.2 Design of the State Observer
5.2.1 Full—Order State Observer
5.2.2 Design of the Full—Order State Observer
5 3 Feedback System with the State Observer
Problems
Chapter6 Discrete Time Control System
6.1 State Space Description of Discrete Time System
6.1.1 State Space Description of Discrete Time System
6.1.2 Obtaining State Space Description from Difference Equation or Impulse Transfer Function
6.1.3 Obtaining Impulse Transfer Function Matrix from State Space Description
6.2 State Equation Solution of Discrete Time LTI System
6.2.1 Iterative Method
6.2.2 z Transform Method
6.2.3 Calculation of the State Transition Matrix
6.3 Data—Sampled Control System
6.3.1 Realization Method
6.3.2 Three Basic Assumptions
6.3.3 Discretization from the State Solution of Cominuous Time System
6.3.4 Approximate Discretization
6.4 Discrete Time System Stability Analysis and Criteria
6.4.1 Lyapunov Stability of Discrete Time System
6.4.2 Lyapunov Stability Theorem of Discrete Time System
6.4.3 Stability Criteria of Discrete Time LTI System
6.5 Controllability and Observability of Discrete Time LTI System
6.5.1 Controllability
6.5.2 Observability
6.5.3 Condition of Remaining Controllability and Observability by Sampling
6.6 Comml Synthesis of Discrete Time LTI System
6.6.1 Design of Poles Placement
6.6.2 State Observer
Problems
Index
References
1.1 Definition of State Space
1.1.2 Definitions
1.1.3 State Space Description
1.1.4 Transfer Function Matrix
1.2 Obtaining State Space Description from I/O Description
1.2.1 Obtaining State Space Description from Differential Equation
1.2.2 Obtaining State Space Description from Transfer Function
1.2.3 Obtaining State Space Description from Block Diagram
1.3 Obtaining Transfer Function Matrix from State Space Description
1.4 Description of Composite Systems
1.4.1 Basic Connection of Composite Systems
1.4.2 Description of the Series Composite Systems
1.4.3 Description of the Parallel Composite Systems
1.4.4 Description of the Feedback Composite Systems
1.5 State Transformation of the LTI system
1.5.1 Eigenvalue and Eigenvector
1.5.2 State Transformation
1.5.3 Invariance Properties of the State Transformation
1.5.4 Obtaining the Diagonal Canonical Form by State Transformation
1.5.5 Obtaining the Jordan Canonical Form by State Transformation
Problems
Chapter2 Time Response of the LTI System
2.1 Time Response of the LTI Homogeneous System
2.2 State Transition Matrix
2.2.1 Definition
2.2.2 Properties of the State Transition Matrix
2.3 Calculation of the Matrix Exponential Function
2.3.1 Direct Method
2.3.2 Laplace Transform Method
2.3.3 Similarity Transformation Method
2.3.4 Cayley—Hamilton Theorem Method
2.4 Time Response of the LTI System
Problems
Chapter3 Stability of the control System
3.1 The Basics of Stability Theory in Mathematics
3.2.1 Equilibrium Point
3.2.2 Concepts of Lyapunov Stability
3.3 Lyapunov Stability Theory
3.3.1 Lyapunov First Method
3.3.2 Lyapunov Second Method
3.4 Application of Lyapunov 2nd Method to the LTI System
3.5 Construction of Lyapunov Function to the
Nonlinear System
Chapter4 Controllability and Observability
4.1 Controllability of The LTI System
4.1.1 Controllability
4.1.2 Criteria of Controllability
4.2 Observability of The LTI System
4.2.1 Observability
4.2.2 Criteria of Observability
4.3 Duality
4.4 Obtaining the Controllable and Observable Canonical Form by State
Transformation
4.4.1 Obtaining the Controllable Canonical Form by State Transformation
4.4.2 Obtaining the Observable Canonical Form by State Transformation
4.5 Canonical Decomposition of the LTI System
4.5.1 Controllable Canonical Decomposition
4.5.2 Observable Canonical Decomposition
4.5.3 Canonical Decomposition
4.6 Minimal Realization of the LTI System
4.6.1 Realization Problem
4.6.2 Realization of SISO System
4.6.3 Realization of MIMO System
4.6.4 Minimal Realization
Problems
Chapter5 Synthesis of the LTI System
5.1 State Feedback Control of the LTI System
5.1.1 State Feedback
5.1.2 Controllability and Observability of the Closed—Loop System
5.1.3 Poles Placement by State Feedback Control
5.1.4 Zeros of the Closed—Loop System
5.2 Design of the State Observer
5.2.1 Full—Order State Observer
5.2.2 Design of the Full—Order State Observer
5 3 Feedback System with the State Observer
Problems
Chapter6 Discrete Time Control System
6.1 State Space Description of Discrete Time System
6.1.1 State Space Description of Discrete Time System
6.1.2 Obtaining State Space Description from Difference Equation or Impulse Transfer Function
6.1.3 Obtaining Impulse Transfer Function Matrix from State Space Description
6.2 State Equation Solution of Discrete Time LTI System
6.2.1 Iterative Method
6.2.2 z Transform Method
6.2.3 Calculation of the State Transition Matrix
6.3 Data—Sampled Control System
6.3.1 Realization Method
6.3.2 Three Basic Assumptions
6.3.3 Discretization from the State Solution of Cominuous Time System
6.3.4 Approximate Discretization
6.4 Discrete Time System Stability Analysis and Criteria
6.4.1 Lyapunov Stability of Discrete Time System
6.4.2 Lyapunov Stability Theorem of Discrete Time System
6.4.3 Stability Criteria of Discrete Time LTI System
6.5 Controllability and Observability of Discrete Time LTI System
6.5.1 Controllability
6.5.2 Observability
6.5.3 Condition of Remaining Controllability and Observability by Sampling
6.6 Comml Synthesis of Discrete Time LTI System
6.6.1 Design of Poles Placement
6.6.2 State Observer
Problems
Index
References