ContentsPrefaceChapter 0 Backgrounds 10.1 Development of Control Theory 10.2 Main Contents of Modern Control Theory 2Chapter 1 Mathematical Description of Systems 41.1 Example 41.2 Basic Definitions 51.3 System Descriptions 61.4 Finding State Equations from High-Differential Operator Representation . 71.4.1 Controllable Canonical Form 71.4.2 Observable Canonical Form 91.4.3 Other Special Form 91.5 Block Diagram 111.6 Transfer Function from State Space Representation 121.6.1 Definition 121.6.2 Calculation for the Transfer Function Matrix 131.7 Composite Systems 141.7.1 Tandem Connection 151.7.2 Parallel Connection 161.7.3 Feedback Connection 171.8 Equivalent Transformation 171.8.1 Equivalent Transformation of the State Space Description for LinearSystems 171.8.2 Diagonal Canonical Form and Jordan Canonical Form of the System 181.8.3 Invariance of the System Matrix and Transfer Function Matrix 201.9 Application of MATLAB in the Representation of Linear Systems 211.10 Exercises 25Chapter 2 Solutions 272.1 State Transition Matrix 272.2 Matrix Exponential 30 2.5.1 Discretization of Linear Discrete Time-Invariant Systems 412.5.2 Solutions of the Linear Discrete Time-Invariant Systems 432.6 MATLAB for Linear System Motion Analysis 432.7 Exercises 47Chapter 3 Controllability and Observability 493.1 Definitions 49 3.1.1 Controllability 50 3.1.2 Observability 503.2 Con trollability of Linear Continuous Systems 51 3.2.1 Time-Invariant Systems 51 3.2.2 Time-Varying Systems 57 3.2.3 Controllability Index 573
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