Abstract
We assume, for a distributed parameter control system, that a linear stabilizing is available. We then seek a stabilizing, necessarily nonlinear, subject to an a priori bound on the control.
Highlights
We are concerned with feedback stabilization of a linear system x_ = Ax for which it is known that the solution semigroup S( ) generated by the operator A is a contraction semigroup on the Hilbert space H
For every solution of (4) one has x(t) ! 0 as t ! 1: Our principal concern here is that the control actuation (2) might be available only subject to a control constraint: kz(t)k 1
Let A be the in nitesimal generator of a C0 contraction semigroup continuous
Summary
Quite di erent in spirit, covered by this hypothesis, would be a di usion problem in which, in a context of no- ux boundary conditions, A has a nontrivial nullspace so some additional dissipation would be needed for asymptotic stability. This is clearly dissipative and, even with a 0, one expects (5) for nontrivial b by results of scattering theory | a uniform stabilization rate would necessarily depend on the support of b( ). Note that this A will not have compact resolvent and if the support of a is small this term will not give stability without the feedback
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