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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005453
URN to cite this document: urn:nbn:de:bvb:703-epub-5453-3

Title data

Grüne, Lars:
Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations.
Bayreuth , 1999

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Abstract

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:	Preprint, postprint
Additional notes (visible to public):	erschienen In: Systems & Control Letters. Bd. 38 (September 1999) Heft 1 . - S. 27-35
Keywords:	Input-to-state stability; Stabilizing feedback control; Robustness
DDC Subjects:	500 Science 500 Science > 510 Mathematics
Institutions of the University:	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 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)
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-5453-3
Date Deposited:	06 May 2021 11:27
Last Modified:	06 May 2021 11:27
URI:	https://epub.uni-bayreuth.de/id/eprint/5453

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