On input-to-state stabilizability of semilinear control systems

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Grüne, Lars:
On input-to-state stabilizability of semilinear control systems.
In: Beghi, Alessandro (Hrsg.): Mathematical theory of networks and systems : Proceedings of the MTNS 98 Symposium held in Padova, Italy, July 1998. - Padova : Il Poligrafo , 1998 . - S. 181-184
ISBN 88-7115-117-8

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Abstract

In this paper we investigate the robustness of state feedback stabilized semilinear control systems subject to inhomogeneous perturbations in terms of input-to-state stability. In particular we are interested in the robustness of an optimal control based exponentially stabilizing discontinuous sampled discrete feedback, which is known to exist whenever the system under consideration is asymptotically null controllable. For this purpose we introduce a robustness condition that will turn out to be equivalent to a suitable input-to-state stability formulation. Validating this condition for the optimal control based feedback using a suitable Lyapunov function we obtain an equivalence between (open loop) asymptotic null controllability and robust input-to-state (state feedback) stabilizability.