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

Title data

Grüne, Lars:
Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations.
In: Systems & Control Letters. Vol. 38 (September 1999) Issue 1 . - pp. 27-35.
ISSN 1872-7956
DOI: https://doi.org/10.1016/S0167-6911(99)00044-4

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Abstract in another language

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 sufficient 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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Input-to-state stability; Stabilizing feedback control; Robustness
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Feb 2021 07:09
Last Modified: 06 May 2021 11:27
URI: https://eref.uni-bayreuth.de/id/eprint/63213