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Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function. (English) Zbl 1133.93358
Summary: The problem of exponential stability and stabilization for a class of uncertain linear time-varying systems is considered. The system matrix belongs to a polytope and the time-varying parameter as well as its time derivative are bounded. Based on a time-varying version of Lyapunov stability theorem, new sufficient conditions for the exponential stability and stabilization via parameter dependent state feedback controllers (i.e., a gain scheduling controllers) are given. Using parameter dependent Lyapunov function, the conditions are formulated in terms of two linear matrix inequalities without introducing extra useless decision variables and hence are simply verified. The results are illustrated by numerical examples.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D09 Robust stability
93C41 Control/observation systems with incomplete information
93B52 Feedback control
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