Observation and Control for Operator SemigroupsThis book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. It includes a large number of examples coming mostly from partial differential equations. |
Contents
1 | 11 |
Operator Semigroups | 33 |
11 | 49 |
9 | 56 |
7 | 66 |
2 | 82 |
4 | 126 |
Testing Admissibility | 139 |
7 | 226 |
8 | 233 |
1 | 261 |
3 | 270 |
6 | 284 |
3 | 295 |
Boundary Control Systems | 317 |
11 | 320 |
4 | 157 |
5 | 164 |
Observability | 173 |
15 | 179 |
4 | 190 |
8 | 201 |
4 | 202 |
8 | 205 |
6 | 211 |
10 | 217 |
Observation for the Wave Equation | 225 |
4 | 330 |
Some Background on Functional Analysis | 385 |
Banach spacevalued LP functions | 399 |
0 | 435 |
Unique Continuation for Elliptic Operators | 445 |
Bibliography | 467 |
| 475 | |
| 479 | |
| 480 | |
Other editions - View all
Observation and Control for Operator Semigroups Marius Tucsnak,George Weiss No preview available - 2009 |
Common terms and phrases
A₁ According to Proposition According to Remark admissible control operator admissible observation operator assume Banach space boundary control system bounded C(sI C₁ Carleson measure clos compact condition continuous embedding convergent Corollary corresponding D(Ao defined Definition denote dense diagonalizable Dirichlet Laplacian domain dual dx dt E D(A eigenvalues eigenvectors equivalent estimate exact exactly observable Example exists fact follows from Proposition formula function H₁ H²(N hence Hilbert space holds implies inequality infinite-time admissible inner product input introduce L²(N Laplace transform Lemma linear m-dissipative Moreover notation obtain open set open subset orthonormal basis pair PDEs pivot space Proof result satisfies Section self-adjoint semigroup sequence skew-adjoint Sobolev spaces solution strictly positive strongly continuous strongly continuous semigroup subspace unique unitary group wave equation X₁ ὃν მო