Practical stabilization of a class of nonlinear systems with partially known uncertainties. (English) Zbl 0825.93650

Summary: In this paper we deal with robust control of a class of nonlinear systems which contain uncertainties. It can be viewed as an extension of the work in [M. J. Corless and G. Leitmann, IEEE Trans. Autom. Control 26, 1139–1144 (1981; Zbl 0473.93056)] for the cases where the vector of uncertainties is only partially known. To cope with the uncertainties, an adaptive controller using a dead-zone and a hysteresis function is proposed and both the uniform boundedness of all the closed-loop signals and uniform ultimate boundedness of the system state are guaranteed. In contrast with some previous attempts to relax the a priori knowledge on the uncertainties bounds by using a discontinuous control law, we propose continuous control laws in this paper. Hence, chattering problems (which have practical importance) can be avoided.


93D21 Adaptive or robust stabilization
93B51 Design techniques (robust design, computer-aided design, etc.)
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93D30 Lyapunov and storage functions


Zbl 0473.93056
Full Text: DOI


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