Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0945.34039
Bhat, Sanjay P.; Bernstein, Dennis S.
Finite-time stability of continuous autonomous systems. (English)
[J] SIAM J. Control Optimization 38, No.3, 751-766 (2000). ISSN 0363-0129; ISSN 1095-7138/e

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.

MSC 2000:: *34D30 Structural stability of ODE
34D20 Lyapunov stability of ODE
93D05 Lyapunov and other classical stabilities of control systems
34A36 Discontinuous equations
93B35 Sensitivity (robustness) of control systems
37C20 Generic properties, structural stability

Keywords: stability; finite-time stability; non-Lipschitzian dynamics; sensitivity

Cited in: Zbl 1217.93136

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]