1 Mathematical Description
1．1 Examples
1．1．1 An RLC Network
1．1．2 A Moving Body System
1．2 System Description
1．2．1 Differential Operator Representation
1．2．2 Transfer Matrix Representation
1．2．3 State Space Representation
1．3 Obtaining State Equations
1．3．1 Finding State Equations from Differential Operator Representation
1．3．2 Finding the State Equation from Transfer Function
1．4 Obtaining Transfer Function Matrix from State Equations
1．5 Mathematical Description of Composite Systems
1．5．1 Parallel Connection
1．5．2 Tandem Connection
1．5．3 Feedback Connection
1．6 Equivalent Systems
1．7 Problems
2 Solutions of Linear Dynamical Systems
2．1 Time-Invariant Homogeneous Systems
2．2 Matrix Exponential ．．．．．．．．
2．2．1 Properties of the Matrix Exponential
2．2．2 The Matrix Exponential for Common Matrices
2．2．3 Calculations ofthe Matrix Exponential
2．3 Time-varying Homogeneous Systems
2．4 Solutions of Linear Dynamical Systems
2．4．1 Linear Time-varying Dynamical Systems
2．4．2 Linear Time-invariant Dynamical Systems
2．5 Problems
3 Controllability and Observability
3．1 Introduction
3 ．2 Definitions
3．2．1 Controllability
3．2．2 Observability
3．3 Linear Time-invariant Systems with Distinct Eigenvalues
3．4 Linear Time-invariant Systems with Arbitrary Eigenvalues
3．5 Linear Time-varying Systems
3．6 Illustrative Problems
3．7 CanonicaI Decomposition
3．7．1 Controllability Decomposition
3．7．2 Observability Decomposition
3．7．3 Canonical Decomposition Theorem
3．7．4 Irreducible Dynamical Equation
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4 Stability of Linear Systems
5 State Feedback and Estimator
6 Optimal Control Theory
7 Irreducible Realizations
Index
References
