Control Theory for Linear Systems

Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems. It treats a wide range of control synthesis problems for linear state space systems with inputs and outputs. The book provides a treatment of these problems using state space methods, often with a geometric flavour. Its subject matter ranges from controllability and observability, stabilization, disturbance decoupling, and tracking and regulation, to linear quadratic regulation, H2 and H-infinity control, and robust stabilization. Each chapter of the book contains a series of exercises, intended to increase the reader' s understanding of the material. Often, these exercises generalize and extend the material treated in the regular text.

1 Introduction. - 2 Mathematical preliminaries. - 3 Systems with inputs and outputs. - 4 Controlled invariant subspaces. - 5 Conditioned invariant subspaces. - 6(C, A, B)-pairs and dynamic feedback. - 7 System zeros and the weakly unobservable subspace. - 8 System invertibility and the strongly reachable subspace. - 9 Tracking and regulation. - 10 Linear quadratic optimal control. - 11 The H2 optimal control problem. - 12 H? control and robustness. - 13 The state feedback H? control problem. - 14 The H? control problem with measurement feedback. - 15 Some applications of the H? control problem. - A Distributions. - A. 1 Notes and references.