图书简介

1 Introduction; 1.1 Introduction; 1.2 Overview; 1.2.1 A brief history; 2 Mathematical Descriptions of Systems; 2.1 Introduction; 2.2 Causality, lumpedness, and time-invariance; 2.2.1 Impulses; 2.3 Linear time-invariant (LTI) systems; 2.3.1 Multi-input multi-output case; 2.4 Linear time-varying systems; 2.3.1 Linearization; 2.5 RLC circuits { Comparisons of various descriptions; 2.6 Mechanical and hydraulic systems; 2.7 Proper rational transfer functions; 2.8 Discrete-time linear time-invariant systems; 2.9 Concluding remarks; Problems; 3 Linear Algebra; 3.1 Introduction; 3.2 Basis, representation, and orthonormalization; 3.3 Linear algebraic equations; 3.4 Similarity transformation; 3.5 Diagonal form and Jordan form; 3.6 Functions of a square matrix; 3.7 Lyapunov equation; 3.8 Some useful formula; 3.9 Quadratic form and positive de niteness; 3.10 Singular value decomposition; 3.11 Norms of matrices; Problems; 4 State-Space Solutions and Realizations; 4.1 Introduction; 4.2 General solution of CT LTI state-space equations; 4.2.1 Discretization; 4.2.2 General solution of DT LTI state-space equations; 4.3 Computer computation of CT state-space equations; 4.3.1 Real-time processing; 4.3.2 Op-amp circuit implementation; 4.4 Equivalent state equations; 4.4.1 Canonical forms; 4.3.2 Magnitude scaling in op-amp circuits; 4.5 Realizations; 4.5.1 Multi-input multi-output case; 4.6 Solution of linear time-varying (LTV) equations; 4.6.1 Discrete-time case; 4.7 Equivalent time-varying equations; 4.8 Time-varying realizations; Problems; 5 Stability; 5.1 Introduction; 5.2 Input-output stability of LTI systems; 5.3 Discrete-time case; 5.4 Internal stability; 5.4.1 Discrete-time case; 5.5 Lyapunov theorem; 5.5.1 Discrete-time case; 5.6 Stability of LTV systems; Problems; 6 Controllability and Observability; 6.1 Introduction .; 6.2 Controllability; 6.2.1 Controllability indices; 6.3 Observability; 6.3.1 Observability indices; 6.4 Canonical decomposition; 6.5 Conditions in Jordan-form equations; 6.6 Discrete-time state-space equations .; 6.6.1 Controllability to the origin and reachability; 6.7 Controllability after sampling; 6.8 LTV state-space equations; Problems; 7 Minimal Realizations and Coprime Fractions; 7.1 Introduction; 7.2 Implications of coprimeness; 7.2.1 Minimal realizations; 7.2.2 Complete characterization; 7.3 Computing coprime fractions; 7.3.1 QR decomposition; 7.4 Balanced realization; 7.5 Realizations from Markov parameters; 7.6 Degree of transfer matrices; 7.7 Minimal realizations{Matrix case; 7.8 Matrix polynomial fractions; 7.8.1 Column and row reducedness; 7.8.2 Computing matrix coprime fractions; 7.9 Realization from matrix coprime fractions; 7.10 Realizations from matrix Markov parameters; 7.11 Concluding remarks; Problems; 8 State Feedback and State Estimators; 8.1 Introduction; 8.2 State feedback; 8.2.1 Solving Lyapunov equation; 8.3 Regulation and tracking; 8.3.1 Robust tracking and disturbance rejection; 8.3.2 Stabilization; 8.4 State estimator; 8.4.1 Reduced-dimensional state estimator; 8.5 Feedback from estimated states .; 8.6 State feedback{MIMO case; 8.6.1 Cyclic design; 8.6.2 Lyapunov-equation method; 8.6.3 Canonical-form method; 8.6.4 E ect on transfer matrices; 8.7 State estimators{MIMO case; 8.8 Feedback from estimated states{MIMO case; Problems; 9 Pole Placement and Model Matching; 9.1 Introduction; 9.2 Preliminary { Matching coe cients; 9.2.1 Compensator equation{Classical method; 9.3 Unity-feedback con guration{Pole placement; 9.3.1 Regulation and tracking; 9.3.2 Robust tracking and disturbance rejection; 9.3.3 Embedding internal models; 9.4 Implementable transfer functions; 9.4.1 Model matching{Two-parameter con guration; 9.4.2 Implementation of two-parameter compensators; 9.5 MIMO unity feedback systems; 9.5.1 Regulation and tracking; 9.5.2 Robust tracking and disturbance rejection; 9.6 MIMO model matching{Two-parameter con guration; 9.6.1 Decoupling; 9.7 Concluding remarks; Problems; References; Answers to Selected Problems; Index

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