An improved LMI-based approach for stability of piecewise affine time-delay systems with uncertainty |
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| Authors: | Shiming Duan Jun Ni A. Galip Ulsoy |
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| Affiliation: | 1. Department of Mechanical Engineering , University of Michigan , Ann Arbor , MI , USA duansm@umich.edu;3. Department of Mechanical Engineering , University of Michigan , Ann Arbor , MI , USA |
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| Abstract: | The stability problem for uncertain piecewise affine (PWA) time-delay systems is investigated in this article. It is assumed that there exists a known constant time delay in the system and the uncertainly is norm-bounded. Sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the Lyapunov–Krasovskii functional with a triple integration term. This approach handles switching based on the delayed states (in addition to the states) for a PWA time-delay system, considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches. The effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples. |
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| Keywords: | piecewise affine systems time-delay systems stability analysis Lyapunov–Krasovskii functional |
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