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Zbl 1131.93043
Moulay, Emmanuel; Perruquetti, Wilfrid
Finite time stability and stabilization of a class of continuous systems. (English)
[J] J. Math. Anal. Appl. 323, No. 2, 1430-1443 (2006). ISSN 0022-247X

The paper deals with systems of ODE's in finite-dimensional space having unique solutions in forward time. It discusses finite-time stability, i.e., the strong version of asymptotic stability when the systems reaches the equilibrium point. The contains two main results. The first result shows that, under appropriate assumptions, existence of a Lyapunov function plus a certain integral property are necessary and sufficient for finite time stability of a system of ODE's. The second result shows that a control-affine system admits a feedback making it finite time stable if and only if there exists a control Lyapunov function satisfying a certain differential inequality. In that case, the finite time stabilizing feedback is given in explicit form.
[Manuel C. Guerra (Lisboa)]

MSC 2000:: *93D15 Stabilization of systems by feedback
93D30 Scalar and vector Lyapunov functions
93C10 Nonlinear control systems
93C15 Control systems governed by ODE

Keywords: finite time stability; Lyapunov function; finite time stabilization; Control Lyapunov function

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Zentralblatt MATH Berlin [Germany]