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Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations

✍ Scribed by Lars Grüne

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
130 KB
Volume
38
Category
Article
ISSN
0167-6911

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✦ Synopsis

In this paper we investigate the robustness of state feedback stabilized semilinear systems subject to inhomogeneous perturbations in terms of input-to-state stability. We consider a general class of exponentially stabilizing feedback controls which covers sampled discrete feedbacks and discontinuous mappings as well as classical feedbacks and derive a necessary and su cient condition for the corresponding closed-loop systems to be input-to-state stable with exponential decay and linear dependence on the perturbation. This condition is easy to check and admits a precise estimate for the constants involved in the input-to-state stability formulation. Applying this result to an optimal control based discrete feedback yields an equivalence between (open-loop) asymptotic null controllability and robust input-to-state (state feedback) stabilizability.

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