Bhat, Sanjay P.; Bernstein, Dennis S. Finite-time stability of continuous autonomous systems. (English) Zbl 0945.34039 SIAM J. Control Optimization 38, No. 3, 751-766 (2000). Summary: 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. Cited in 1 ReviewCited in 1187 Documents MSC: 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 34A36 Discontinuous ordinary differential equations 93B35 Sensitivity (robustness) 37C20 Generic properties, structural stability of dynamical systems Keywords:stability; finite-time stability; non-Lipschitzian dynamics; sensitivity × Cite Format Result Cite Review PDF Full Text: DOI