Linear Operators and Linear Systems: An Analytical Approach to Control Theory (London Mathematical Society Student Texts)

Description

This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be suitable for a course in functional analysis. The book also includes applications to partial differential equations, the stability and stabilization of linear systems, power signal spaces, and delay systems, treated from an input/output point of view. Cover......Page 1 Title Page......Page 4 Copyright......Page 5 Contents......Page 6 Preface......Page 8 1.1 Banach spaces and bounded operators......Page 12 1.2 Hardy spaces on the disc and half-plane......Page 15 1.3 Inner and outer functions......Page 19 1.4 Vector-valued Hardy spaces......Page 24 2.1 The graph of an operator......Page 28 2.2 Semigroups......Page 33 2.3 The gap metric......Page 41 3.1 Invariant subspaces......Page 48 3.2 Invariant operators......Page 55 3.4 Causality......Page 60 3.4 The commutant lifting theorem......Page 64 4.1 Stability theory......Page 74 4.2 Robustness......Page 83 4.3 The chordal metric......Page 92 5.1 Almost-periodic functions......Page 100 5.2 Power signal spaces......Page 116 5.3 Spectral distribution functions......Page 120 6.1 Background and classification......Page 132 6.2 Stability......Page 140 6.3 Rational approximation......Page 145 6.4 Stabilization......Page 155 Bibliography......Page 162 Index......Page 173