Foundation of modern control theory

　　Section Ⅰ State Space Analysis and Synthesis of Linear Systems
　　 State Space Description of Dynamic Systems
　　 1.1 Introduction
　　 1.2 State and state space
　　 1.3 State space description of dynamic systems
　　 1.4 Canonical form of SISO state space representation
　　 1.4.1 Controllable canonical form
　　 1.4.2 Observable canonical form
　　 1.4.3 Diagonal form and Jordan canonical form
　　 1.5 Some examples of developing state space descriptions
　　 1.6 Equivalent state equations
　　 1.6.1 Similarity transformation
　　 1.6.2 An application of similarity transformation--
　　 Diagonal form and Jordan form
　　 1.7 Relationship between I/O description and state-space
　　 description
　　 1.7.1 Transfer function from state-space description
　　 1.7.2 State-space representations from transfer functions--
　　 Realizations
　　 Problems
　　 Solution of State Equations of Linear Systems
　　 2.1 Introduction
　　 2.2 Solution of linear homogeneous state equation
　　 2.3 Properties and calculations of the matrix exponential function
　　 2.3.1 Properties of □
　　 2.3.2 Calculation of □
　　 2.4 Solution of state equations
　　 2.5 State transition matrix of linear time-invariant systems
　　 Problems
　　 Controllability and Observability
　　 3.1 Introduction
　　 3.2 Controllability
　　 3.2.1 Definition of complete state controllability
　　 3.2.2 Controllability criterion for time-invariant systems with arbitrary eigenvalues
　　 3.2.3 Controllability criterion for time-invariant systems with distinct □genvalues
　　 3.2.4 Controllability criterions for time-invariant systems with
　　 multi-eigenvalues
　　 3.3 Observability
　　 3.3.1 Definition of complete state observability
　　 3.3.2 Observability criterion for time-invariant systems with arbitrary eigenvalues
　　 3.3.3 Observability criterion for time-invariant systems with distinct eigenvalues
　　 3.3.4 Observability criterion for time-invariant systems with multi-eigenvalues
　　 3.4 Principle of duality
　　 3.5 Obtaining the controllable and observable canonical
　　 forms for SISO systems
　　 3.5.1 Controllable canonical form of SISO systems
　　 3.5.2 Observable canonical form of SISO systems
　　 3.6 Canonical decomposition
　　 3.6.1 Decomposition according to controllability
　　 3.6.2 Decomposition according to observability
　　 3.6.3 Canonical structure of system
　　 Extensions and Proofs
　　 Problems
　　 Desigh of State Feedback Control Systems
　　 4.1 Introduction
　　 4.2 State feedback
　　 4.2.1 State feedback scheme
　　 4 2 2 The effect of state feedback on system properties
　　 4.3 Pole assignment using state feedback
　　 4.3.1 Description of pole assignment problem
　　 4.3.2 Necessary and sufficient condition for arbitrary pole assignment
　　 4.3 3 Pole assignment via control canonical form of state equations
　　 4.3.4 Pole assignment via Ackermann's formula
　　 4.3.5 Direct calculation of gains by comparing characteristic equations
　　 4.4 Design of state observers
　　 4.5 Feedback from estimated states
　　 Problems
　　Section Ⅱ Linear Discrete-time Systems
　　 5 Discrete-time Systems and Computer Control Systems
　　 5.1 Introduction
　　 5.2 Sample-data control and computer control systems
　　 5.3 Related theories
　　 5.4 Sampling process and sample theorem
　　 5.5 The z transform
　　 5.6 The computation of z transform and the z transform of elementary functions
　　 5.7 Important properties of the z transform
　　 5.8 The inverse z transform
　　 5.9 Difference equation
　　 5.10 The z transform method for solving difference equations
　　 5.11 The model of a discrete-time control system and the pulse transfer function
　　 5.12 The difference equation and pulse transfer function
　　 Problems
　　 Analysis and Design of Discrete-Time Control Systems
　　 6.1 Introduction
　　 6.2 Mapping between the s plane and the z plane
　　 6.3 Stability analysis of closed-loop systems in the z plane
　　 6.4 Steady-state response analysis
　　 6.5 The dynamic analysis for the control system in the z plane
　　 6.6 The design of the discrete-time compensator
　　 6.6.1 Dead-beat control with intersampling ripples
　　 6.6.2 Dead-beat control without intersampling ripples
　　 6.6.3 Shortcomings of the Dead-beat control
　　 6.7 Realization of digital controller
　　 Problems
　　Section Ⅲ Nonlinear Systems
　　 Introduction to Nonlinear Control Systems
　　 7.1 Introduction
　　 7.2 Common nonlinear elements
　　 7.3 Properties of nonlinear systems
　　 7.3.1 Classification of nonlinearities
　　 7.3.2 Some common nonlinear system behaviors
　　 7.4 Approaches to the analysis of nonlinear control systems
　　 Describing Function Analysis
　　 8.1 Introduction
　　 8.2 Describing function fundamentals
　　 8.2.1 Basic assumptions
　　 8.2.2 Basic definitions
　　 8.2.3 Computing describing functions
　　 8.3 Describing functions of common nonlinearities
　　 8.4 Describing function analysis of nonlinear system
　　 8.4.1 Prediction and stability of self oscillations
　　 8.4.2 Plot of curves of G(□) and -□
　　 8.4.3 Reliability of the describing function method
　　 8.5 Conclusion
　　 Problems
　　 Phase Plane Analysis
　　 9.1 Introduction
　　 9.2 Basic ideas of phase plane analysis
　　 9.3 Characteristics of phase plane trajectories
　　 9.4 Constructing phase portraits
　　 9.4.1 The method of isoclines
　　 9.4.2 Analytical method
　　 9.5 Phase plane analysis of nonlinear systems
　　 9.5.1 Linearization of nonlinear system
　　 9.5.2 Phase trajectories for linear systems
　　 9.6 Conclusions
　　 Problems
　　 10 Lyapunov Stability Theory
　　 10.1 Introduction
　　 10.2 Equilibrium states and concepts of stability
　　 10.2.1 Equilibrium state
　　 10.2.2 Concepts of lyapunov stability
　　 10.3 Lyapunov's linearization method
　　 10.4 Lyapunov's direct method
　　 10.4.1 Basic idea
　　 10.4.2 Some concepts of singular scalar functions
　　 10.4.3 Lyapunov's stability theorems
　　 10.5 Construction of Lyapunov function
　　 10.5.1 Lyapunov equation
　　 10.5.2 The variable gradient method (Schultz-Gilbson method)
　　 10.5.3 Aiserman method
　　 10.6 Conclusions
　　 Problems
　　References