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Fast finite-time stability and its application in adaptive control of high-order nonlinear system. (English) Zbl 1429.93323

Summary: This paper addresses the problem of global finite-time adaptive stabilization for a class of high-order uncertain nonlinear systems. A new finite-time stability result is established to provide a less conservative estimation of convergent time in uncertain situation, and a state feedback stabilizer with an adaptive mechanism is constructed by applying continuous domination to adaptive fashion of the systems to be considered. The main novelty of this paper is the skillful development of an analytic strategy and the delicate selection of Lyapunov functions in searching for the adaptive fast finite-time stabilizer. A benchmark example is given to demonstrate the effectiveness of the proposed strategy.

MSC:

93D40 Finite-time stability
93D21 Adaptive or robust stabilization
93D15 Stabilization of systems by feedback
93C40 Adaptive control/observation systems
93C41 Control/observation systems with incomplete information
93C10 Nonlinear systems in control theory
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