State Space and Input-Output Linear Systems

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. 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