Preface
Chapter 0 Backgrounds 1
0.1 Development of Control Theory 1
0.2 Main Contents of Modern Control Theory 2
Chapter 1 Mathematical Description of Systems 4
1.1 Example 4
1.2 Basic Definitions 5
1.3 System Descriptions 6
1.4 Finding State Equations from High-Differential Operator Representation . 7
1.4.1 Controllable Canonical Form 7
1.4.2 Observable Canonical Form 9
1.4.3 Other Special Form 9
1.5 Block Diagram 11
1.6 Transfer Function from State Space Representation 12
1.6.1 Definition 12
1.6.2 Calculation for the Transfer Function Matrix 13
1.7 Composite Systems 14
1.7.1 Tandem Connection 15
1.7.2 Parallel Connection 16
1.7.3 Feedback Connection 17
1.8 Equivalent Transformation 17
1.8.1 Equivalent Transformation of the State Space Description for Linear
Systems 17
1.8.2 Diagonal Canonical Form and Jordan Canonical Form of the System 18
1.8.3 Invariance of the System Matrix and Transfer Function Matrix 20
1.9 Application of MATLAB in the Representation of Linear Systems 21
1.10 Exercises 25
Chapter 2 Solutions 27
2.1 State Transition Matrix 27
2.2 Matrix Exponential 30
2.5.1 Discretization of Linear Discrete Time-Invariant Systems 41
2.5.2 Solutions of the Linear Discrete Time-Invariant Systems 43
2.6 MATLAB for Linear System Motion Analysis 43
2.7 Exercises 47
Chapter 3 Controllability and Observability 49
3.1 Definitions 49
3.1.1 Controllability 50
3.1.2 Observability 50
3.2 Controllability of Linear Continuous Systems 51
3.2.1 Time-Invariant Systems 51
3.2.2 Time-Varying Systems 57
3.2.3 Controllability Index 57
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