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.

The connection of geometric control theory to H2 and H-infinity optimal control theory provides an additional insight for the reader The authors have all contributed at different times to the development of the theory presented in the book: Malo Hautus was involved in the development of the fundamental concepts of linear system theory. Harry Trentelman was a major contributor to the development of almost invariant subspaces, and Anton Stoorvogel helped to establish the connection between geometric control and H2 and H-infinity optimal control

Texte du rabat

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.

Résumé
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.

Contenu
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.