Linear System Theory and Design

Hardcover | November 28, 2012

byChi-Tsong Chen

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Striking a balance between theory and applications, Linear System Theory and Design, Fourth Edition, uses simple and efficient methods to develop results and design procedures that students can readily employ. Ideal for advanced undergraduate courses and first-year graduate courses in linearsystems and multivariable system design, it is also a helpful resource for practicing engineers.

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Striking a balance between theory and applications, Linear System Theory and Design, Fourth Edition, uses simple and efficient methods to develop results and design procedures that students can readily employ. Ideal for advanced undergraduate courses and first-year graduate courses in linearsystems and multivariable system design, it i...

Chi-Tsong Chen is Professor Emeritus of Electrical and Computer Engineering at Stony Brook University, New York.

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Format:HardcoverDimensions:400 pages, 9.25 × 7.5 × 0.98 inPublished:November 28, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199959579

ISBN - 13:9780199959570

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Table of Contents

1. Introduction1.1 Introduction1.2 Overview1.2.1 A brief history2. Mathematical Descriptions of Systems2.1 Introduction2.2 Causality, lumpedness, and time-invariance2.2.1 Impulses2.3 Linear time-invariant (LTI) systems2.3.1 Multi-input multi-output case2.4 Linear time-varying systems2.4.1 Linearization2.5 RLC circuits { Comparisons of various descriptions2.6 Mechanical and hydraulic systems2.7 Proper rational transfer functions2.8 Discrete-time linear time-invariant systems2.9 Concluding remarksProblems3. Linear Algebra3.1 Introduction3.2 Basis, representation, and orthonormalization3.3 Linear algebraic equations3.4 Similarity transformation3.5 Diagonal form and Jordan form3.6 Functions of a square matrix3.7 Lyapunov equation3.8 Some useful formula3.9 Quadratic form and positive de_niteness3.10 Singular value decomposition3.11 Norms of matricesProblems4. State-Space Solutions and Realizations4.1 Introduction4.2 General solution of CT LTI state-space equations4.2.1 Discretization4.2.2 General solution of DT LTI state-space equations4.3 Computer computation of CT state-space equations4.3.1 Real-time processing4.3.2 Op-amp circuit implementation4.4 Equivalent state equations4.4.1 Canonical forms4.4.2 Magnitude scaling in op-amp circuits4.5 Realizations4.5.1 Multi-input multi-output case4.6 Solution of linear time-varying (LTV) equations4.6.1 Discrete-time case4.7 Equivalent time-varying equations4.8 Time-varying realizationsProblems5. Stability5.1 Introduction5.2 Input-output stability of LTI systems5.3 Discrete-time case5.4 Internal stability5.4.1 Discrete-time case5.5 Lyapunov theorem5.5.1 Discrete-time case5.6 Stability of LTV systemsProblems6. Controllability and Observability6.1 Introduction6.2 Controllability6.2.1 Controllability indices6.3 Observability6.3.1 Observability indices6.4 Canonical decomposition6.5 Conditions in Jordan-form equations6.6 Discrete-time state-space equations .6.6.1 Controllability to the origin and reachability6.7 Controllability after sampling6.8 LTV state-space equationsProblems7. Minimal Realizations and Coprime Fractions7.1 Introduction7.2 Implications of coprimeness7.2.1 Minimal realizations7.2.2 Complete characterization7.3 Computing coprime fractions7.3.1 QR decomposition7.4 Balanced realization7.5 Realizations from Markov parameters7.6 Degree of transfer matrices7.7 Minimal realizations{Matrix case7.8 Matrix polynomial fractions7.8.1 Column and row reducedness7.8.2 Computing matrix coprime fractions7.9 Realization from matrix coprime fractions7.10 Realizations from matrix Markov parameters7.11 Concluding remarksProblems8. State Feedback and State Estimators8.1 Introduction8.2 State feedback8.2.1 Solving Lyapunov equation8.3 Regulation and tracking8.3.1 Robust tracking and disturbance rejection8.3.2 Stabilization8.4 State estimator8.4.1 Reduced-dimensional state estimator8.5 Feedback from estimated states8.6 State feedback{MIMO case8.6.1 Cyclic design8.6.2 Lyapunov-equation method8.6.3 Canonical-form method8.6.4 E_ect on transfer matrices8.7 State estimators{MIMO case8.8 Feedback from estimated states{MIMO caseProblems9. Pole Placement and Model Matching9.1 Introduction9.2 Preliminary { Matching coe_cients9.2.1 Compensator equation{Classical method9.3 Unity-feedback con_guration{Pole placement9.3.1 Regulation and tracking9.3.2 Robust tracking and disturbance rejection9.3.3 Embedding internal models9.4 Implementable transfer functions9.4.1 Model matching{Two-parameter con_guration9.4.2 Implementation of two-parameter compensators9.5 MIMO unity feedback systems9.5.1 Regulation and tracking9.5.2 Robust tracking and disturbance rejection9.6 MIMO model matching{Two-parameter con_guration9.6.1 Decoupling9.7 Concluding remarksProblemsReferencesAnswers to Selected ProblemsIndex