State Space and Input-Output Linear Systems

✍ Scribed by David F. Delchamps (auth.)

• Publisher: Springer-Verlag New York
• Year: 1988
• Tongue: English
• Leaves: 430
• Edition: 1
• Category: Library

✦ Synopsis

It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu­ ate level linear system theory course in the School of Electrical Engineering at Cornell. The members of the class have always come from a variety of departments and backgrounds, and con­ sequently have entered the class with levels of preparation ranging from first year calculus and a taste of transform theory on the one extreme to senior level real analysis and abstract algebra on the other.

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-9
Front Matter....Pages 11-11
Some Linear Algebra....Pages 11-31
Linear Differential Equations: Existence and Uniqueness Theorems....Pages 31-49
Linear Difference Equations....Pages 50-51
Some More Linear Algebra....Pages 52-72
DuaL Spaces, Norms, and Inner Products....Pages 73-88
Front Matter....Pages 89-89
State Space Linear Systems: Formal Definitions and General Properties....Pages 89-103
Realizations....Pages 104-113
Eigenvectors, Eigenvalues, and Normal Modes....Pages 114-131
The M + N Decomposition for Matrices Which Are Not Semi-Simple....Pages 132-144
Complex Matrices and the Unitary Diagonalizabity of Hermitian Matrices....Pages 145-149
Nilpotent Matrices and the Jordan Canonical Form....Pages 150-161
Positive Definiteness, Matrix Factorization, and an Imperfect Analogy....Pages 162-175
Reachability and Controllability for Time-Invariant Continuous-Time Systems....Pages 176-186
Reachability and Controllability for Time-Invariant Discrete-Time Systems....Pages 187-194
Observability for Time-Invariant Continuous-Time Systems....Pages 195-201
Observability and Constructibility for Time-Invariant Discrete-Time Systems....Pages 202-207
The Tie Canonical Structure Theorem....Pages 208-218
Front Matter....Pages 219-219
Formal Definitions and General Properties....Pages 219-235
Frequency Responses and Transfer Functions of Time-Invariant Continuous-Time Systems....Pages 236-249
Front Matter....Pages 219-219
Frequency Responses and Transfer Functions of Time-Invariant Discrete-Time Systems....Pages 250-261
Realizations and McMillan Degree....Pages 262-288
Polynomial Matrices and Matrix Fraction Descriptions....Pages 289-321
Front Matter....Pages 322-322
Stability of State Space Linear Systems....Pages 322-349
Stability of Input-Output Linear Systems....Pages 350-364
Feedback, Observers, and Canonical Forms....Pages 365-392
The Discrete-Time Linear Quadratic Regulator Problem....Pages 393-405
The Continuous-Time Linear Quadratic Regulator Problem....Pages 406-415
Back Matter....Pages 417-419

✦ Subjects

Systems Theory, Control;Electrical Engineering;Communications Engineering, Networks