Mathematical Control Theory: Deterministic Finite Dimensional Systems 2nd ed. 1998, v. 6

Introduces the basic concepts and results of mathematical control and system theory. This book covers what constitutes the common core of control theory: the algebraic theory of linear systems, including controllability, observability, feedback equivalence, and minimality; and stability via Lyapunov, as well as input/output methods.

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

From the reviews "This book will be very useful for mathematics and engineering students interested in a modern and rigorous systems course, as well as for the experts in control theory and applications." MATHEMATICAL REVIEWS

Series Preface		v	(2)
Preface to the Second Edition		vii	(2)
Preface to the First Edition		ix
1 Introduction		1	(24)
1.1 What Is Mathematical Control Theory?		1	(1)
1.2 Proportional-Derivative Control		2	(4)
1.3 Digital Control		6	(3)
1.4 Feedback Versus Precomputed Control		9	(2)
1.5 State-Space and Spectrum Assignment		11	(5)
1.6 Outputs and Dynamic Feedback		16	(4)
1.7 Dealing with Nonlinearity		20	(2)
1.8 A Brief Historical Background		22	(1)
1.9 Some Topics Not Covered		23	(2)
2 Systems		25	(56)
2.1 Basic Definitions		25	(5)
2.2 I/O Behaviors		30	(2)
2.3 Discrete-Time		32	(4)
2.4 Linear Discrete-Time Systems		36	(3)
2.5 Smooth Discrete-Time Systems		39	(2)
2.6 Continuous-Time		41	(5)
2.7 Linear Continuous-Time Systems		46	(7)
2.8 Linearizations Compute Differentials		53	(11)
2.9 More on Differentiability		64	(8)
2.10 Sampling		72	(1)
2.11 Volterra Expansions		73	(3)
2.12 Notes and Comments		76	(5)
3 Reachability and Controllability		81	(60)
3.1 Basic Reachability Notions		81	(3)
3.2 Time-Invariant Systems		84	(8)
3.3 Controllable Pairs of Matrices		92	(7)
3.4 Controllability Under Sampling		99	(5)
3.5 More on Linear Controllability		104	(13)
3.6 Bounded Controls*		117	(5)
3.7 First-Order Local Controllability		122	(6)
3.8 Controllability of Recurrent Nets*		128	(8)
3.9 Piecewise Constant Controls		136	(1)
3.10 Notes and Comments		137	(4)
4 Nonlinear Controllability		141	(42)
4.1 Lie Brackets		141	(6)
4.2 Lie Algebras and Flows		147	(7)
4.3 Accessibility Rank Condition		154	(10)
4.4 Ad, Distributions, and Frobenius' Theorem		164	(13)
4.5 Necessity of Accessibility Rank Condition		177	(2)
4.6 Additional Problems		179	(2)
4.7 Notes and Comments		181	(2)
5 Feedback and Stabilization		183	(78)
5.1 Constant Linear Feedback		183	(6)
5.2 Feedback Equivalence*		189	(8)
5.3 Feedback Linearization*		197	(10)
5.4 Disturbance Rejection and Invariance		207	(4)
5.5 Stability and Other Asymptotic Notions		211	(4)
5.6 Unstable and Stable Modes*		215	(3)
5.7 Lyapunov and Control-Lyapunov Functions		218	(15)
5.8 Linearization Principle for Stability		233	(6)
5.9 Introduction to Nonlinear Stabilization*		239	(17)
5.10 Notes and Comments		256	(5)
6 Outputs		261	(54)
6.1 Basic Observability Notions		261	(7)
6.2 Time-Invariant Systems		268	(8)
6.3 Continuous-Time Linear Systems		276	(4)
6.4 Linearization Principle for Observability		280	(3)
6.5 Realization Theory for Linear Systems		283	(7)
6.6 Recursion and Partial Realization		290	(7)
6.7 Rationality and Realizability		297	(6)
6.8 Abstract Realization Theory*		303	(7)
6.9 Notes and Comments		310	(5)
7 Observers and Dynamic Feedback		315	(32)
7.1 Observers and Detectability		315	(6)
7.2 Dynamic Feedback		321	(5)
7.3 External Stability for Linear Systems		326	(5)
7.4 Frequency-Domain Considerations		331	(6)
7.5 Parametrization of Stabilizers		337	(7)
7.6 Notes and Comments		344	(3)
8 Optimality: Value Function		347	(50)
8.1 Dynamic Programming*		349	(14)
8.2 Linear Systems with Quadratic Cost		363	(8)
8.3 Tracking and Kalman Filtering*		371	(9)
8.4 Infinite-Time (Steady-State) Problem		380	(10)
8.5 Nonlinear Stabilizing Optimal Controls		390	(4)
8.6 Notes and Comments		394	(3)
9 Optimality: Multipliers		397	(26)
9.1 Review of Smooth Dependence		397	(2)
9.2 Unconstrained Controls		399	(10)
9.3 Excursion into the Calculus of Variations		409	(6)
9.4 Gradient-Based Numerical Methods		415	(3)
9.5 Constrained Controls: Minimum Principle		418	(3)
9.6 Notes and Comments		421	(2)
10 Optimality: Minimum-Time for Linear Systems		423	(24)
10.1 Existence Results		424	(7)
10.2 Maximum Principle for Time-Optimality		431	(5)
10.3 Applications of the Maximum Principle		436	(7)
10.4 Remarks on the Maximum Principle		443	(1)
10.5 Additional Exercises		444	(2)
10.6 Notes and Comments		446	(1)
APPENDIXES		447	(46)
A Linear Algebra		447	(14)
A.1 Operator Norms		447	(1)
A.2 Singular Values		448	(4)
A.3 Jordan Forms and Matrix Functions		452	(4)
A.4 Continuity of Eigenvalues		456	(5)
B Differentials		461	(6)
B.1 Finite Dimensional Mappings		461	(2)
B.2 Maps Between Normed Spaces		463	(4)
C Ordinary Differential Equations		467	(26)
C.1 Review of Lebesgue Measure Theory		467	(6)
C.2 Initial-Value Problems		473	(1)
C.3 Existence and Uniqueness Theorem		474	(13)
C.4 Linear Differential Equations		487	(4)
C.5 Stability of Linear Equations		491	(2)
Bibliography		493	(26)
List of Symbols		519	(4)
Index		523

2nd edition