Linear Systems Theory, Second Edition

by ;
Edition: 2nd
Format: Hardcover
Pub. Date: 1997-11-25
Publisher(s): CRC Press
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Summary

This second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more.Linear Systems Theory discusses:o Nonlinear and linear systems in the state space form and through the transfer function methodo Stability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stabilityo Controllabilityo Observabilityo Canonical formso System realizations and minimal realizations, including state space approach and transfer function realizationso System designo Kalman filterso Nonnegative systemso Adaptive controlo Neural networksThe book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences.What's New in the Second Edition?o Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studieso Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chaptero Illustrative examples in all the chapterso An introduction and analysis of new stability conceptso An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first editionAlthough more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material.Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.

Table of Contents

Authors vii(2)
Preface ix(4)
Introduction xiii
1 Mathematical Background
1(56)
1.1 Introduction
1(1)
1.2 Metric Spaces and Contraction Mapping Theory
1(17)
1.2.1 Metric Spaces
2(7)
1.2.2 Mappings in Metric Spaces
9(5)
1.2.3 Contraction Mappings and Fixed Points
14(4)
1.3 Some Properties of Vectors and Matrices
18(35)
1.3.1 Norms of Vectors and Matrices
18(12)
1.3.2 Special Matrix Forms
30(11)
1.3.3 Matrix functions
41(12)
Problems
53(4)
2 Mathematics of Dynamic Processes
57(50)
2.1 Solution of Ordinary Differential Equations
57(32)
2.1.1 Existence and Uniqueness Theorems
57(8)
2.1.2 Solution of Linear Differential Equations
65(10)
2.1.3 Laplace Transform
75(14)
2.2 Solution of Difference Equations
89(14)
2.2.1 General Solutions
89(3)
2.2.2 Solution of Linear Difference Equations
92(3)
2.2.3 Z-transform
95(8)
Problems
103(4)
3 Characterization of Systems
107(90)
3.1 The Concept of Dynamic Systems
107(5)
3.2 Equilibrium and Linearization
112(7)
3.3 Continuous Linear Systems
119(25)
3.3.1 State-Space Approach
119(2)
3.3.2 Transfer Functions
121(4)
3.3.3 Equations in Input-Output Form
125(4)
3.3.4 Combinations
129(11)
3.3.5 Adjoint and Dual Systems
140(4)
3.4 Discrete Systems
144(5)
3.5 Applications
149(42)
3.5.1 Dynamic Systems in Engineering
149(24)
3.5.2 Dynamic Systems in Social Sciences
173(18)
Problems
191(6)
4 Stability Analysis
197(46)
4.1 The Elements of the Lyapunov Stability Theory
198(21)
4.1.1 Lyapunov Functions
199(6)
4.1.2 The stability of time-variant linear systems
205(1)
4.1.3 The Stability of Time-Invariant Linear Systems
206(13)
4.2 BIBO Stability
219(5)
4.3 Applications
224(14)
4.3.1 Applications in Engineering
224(5)
4.3.2 Applications in the Social Sciences
229(9)
Problems
238(5)
5 Controllability
243(50)
5.1 Continuous Systems
243(25)
5.1.1 General Conditions
244(12)
5.1.2 Time-Invariant Systems
256(8)
5.1.3 Output and Trajectory Controllability
264(4)
5.2 Discrete Systems
268(6)
5.3 Applications
274(13)
5.3.1 Dynamic Systems in Engineering
274(7)
5.3.2 Applications in the Social Sciences
281(6)
Problems
287(6)
6 Observability
293(34)
6.1 Continuous Systems
294(9)
6.1.1 General Conditions
294(5)
6.1.2 Time-Invariant Systems
299(4)
6.2 Discrete Systems
303(4)
6.3 Duality
307(3)
6.4 Applications
310(12)
6.4.1 Dynamic Systems in Engineering
310(6)
6.4.2 Applications in the Social Sciences
316(6)
Problems
322(5)
7 Canonical Forms
327(48)
7.1 Diagonal and Jordan Forms
329(4)
7.2 Controllability Canonical Forms
333(9)
7.3 Observability Canonical Forms
342(4)
7.4 Applications
346(23)
7.4.1 Dynamic Systems in Engineering
346(14)
7.4.2 Applications in the Social Sciences and Economics
360(9)
Problems
369(6)
8 Realization
375(50)
8.1 Realizability of Weighting Patterns
376(20)
8.1.1 Realizability Conditions
377(3)
8.1.2 Minimal Realizations
380(7)
8.1.3 Time-Invariant Realizations
387(9)
8.2 Realizability of Transfer Functions
396(11)
8.2.1 Realizability Conditions
397(7)
8.2.2 Minimal Realizations
404(3)
8.3 Applications
407(12)
8.3.1 Dynamic Systems in Engineering
407(5)
8.3.2 Applications in the Social Sciences and Economics
412(7)
Problems
419(6)
9 Estimation and Design
425(38)
9.1 The Eigenvalue Placement Theorem
426(5)
9.2 Observers
431(4)
9.3 Reduced-Order Observers
435(2)
9.4 The Eigenvalue Separation Theorem
437(4)
9.5 Applications
441(16)
9.5.1 Dynamic Systems in Engineering
441(9)
9.5.2 Applications in the Social Sciences and Economics
450(7)
Problems
457(6)
10 Advanced Topics
463(36)
10.1 Nonnegative Systems
463(6)
10.2 The Kalman-Bucy Filter
469(3)
10.3 Adaptive Control Systems
472(12)
10.4 Neural Networks
484(15)
References 499(4)
Index 503

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