Introduction to infinite-dimensional systems theory: a state-space approach

Preface......Page 6
 References......Page 8
Contents......Page 10
 1.1 Motivation......Page 14
 1.2 Systems theory concepts in finite dimensions......Page 20
 1.3 Aims of this book......Page 26
 2.1 Strongly continuous semigroups......Page 29
 2.2 Abstract differential equations......Page 52
 2.3 Contraction and dual semigroups......Page 57
 2.4 Invariant subspaces......Page 63
 2.5 Exercises......Page 71
 2.6 Notes and references......Page 82
 3.1 Spatially invariant semigroups......Page 83
 3.2 Riesz-spectral operators......Page 91
 3.3 Delay equations......Page 121
 3.4 Characterization of invariant subspaces......Page 137
 3.5 Exercises......Page 144
 3.6 Notes and references......Page 161
 4.1 Exponential stability......Page 163
 4.2 Weak and strong stability......Page 176
 4.3 Sylvester equations......Page 183
 4.4 Exercises......Page 188
 4.5 Notes and references......Page 197
 5.1 The abstract Cauchy problem......Page 199
 5.2 Asymptotic behaviour......Page 211
 5.3 Perturbations and composite systems......Page 214
 5.4 Exercises......Page 226
 5.5 Notes and references......Page 231
 6.1 Input and outputs......Page 232
 6.2 Controllability and observability......Page 235
 6.3 Tests for controllability and observability in infinite time......Page 259
 6.4 Input and output stability......Page 275
 6.5 Lyapunov equations......Page 279
 6.6 Exercises......Page 285
 6.7 Notes and references......Page 299
 7.1 Impulse response......Page 301
 7.2 Transfer functions......Page 305
 7.3 Transfer functions and the Laplace transform of the impulse response......Page 316
 7.4 Input-output stability and system stability......Page 320
 7.5 Dissipativity and passivity......Page 330
 7.6 Exercises......Page 338
 7.7 Notes and references......Page 351
 8.1 Exponential stabilizability and detectability......Page 353
 8.2 Tests for exponential stabilizability and detectability......Page 363
 8.3 Compensator design......Page 374
 8.4 Strong stabilizability......Page 380
 8.5 Exercises......Page 383
 8.6 Notes and references......Page 392
 9.1 The problem on a finite-time interval......Page 394
 9.2 The problem on the infinite-time interval......Page 417
 9.3 System properties of the closed-loop system......Page 432
 9.4 Maximal solution to the algebraic Riccati equation......Page 441
 9.5 Linear quadratic optimal control for systems with nonzero feedthrough......Page 454
 9.6 Exercises......Page 458
 9.7 Notes and references......Page 485
 10.1 General formulation......Page 488
 10.2 Transfer functions......Page 496
 10.3 Flexible beams with two types of boundary control......Page 500
 10.4 Exercises......Page 512
 10.5 Notes and references......Page 530
 11.1 Existence and uniqueness of solutions......Page 532
 11.2 Lyapunov stability theory......Page 543
 11.3 Semilinear differential equations with holomorphic Riesz-spectral generators......Page 575
 11.4 Exercises......Page 600
 11.5 Notes and references......Page 615
 A.1 Complex analysis......Page 617
  A.2.1  General theory......Page 624
  A.2.2  Hilbert spaces......Page 630
  A.3.1  General theory......Page 636
  A.3.2  Operators on Hilbert spaces......Page 652
  A.4.1  General spectral theory......Page 668
  A.4.2  Spectral theory for compact normal operators......Page 675
  A.5.1  Measure theory......Page 680
  A.5.2  Integration theory......Page 681
  A.5.3  Differentiation theory......Page 690
  A.6.1  Laplace and Fourier transforms......Page 697
  A.6.2  Frequency-domain spaces......Page 701
  A.6.3  The Hardy spaces......Page 704
  A.6.4  Frequency-domain spaces on the unit disc......Page 710
  A.7.1  General definitions......Page 716
  A.7.2  Coprime factorizations over principal ideal domains......Page 721
  A.7.3  Coprime factorizations over commutative integral domains......Page 727
  A.7.4  The convolution algebras calA(β)......Page 728
 References......Page 735
Index......Page 750