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Finite-Time Stability of Continuous Autonomous Systems
Open accessAbstract
Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Hölder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
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Cited by
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Metadata
- Authors
- Bhat, S. P., & Bernstein, D. S.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 2000-01
- Volume
- 38
- Issue
- 3
- Pages
- 751-766
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W1988837728
- Cited by
- 5,510
- References
- 0
- FWCI
- 16.05
- Type
- journal article
- Language
- en
- Open access
- green
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