Robust stabilizability of linear time varying uncertain dynamical systems via linear feedback control

Abstract

This paper investigates the problem of designing a linear static feedback control to stabilize a class of uncertain linear dynamical systems. The systems under consideration contain time-varying uncertain parameters whose values are unknown but bounded in given compact sets. The method used to establish asymptotical stability of the closed loop system (obtained when the feedback control is applied) involves the use of a quadratic Lyupunov function. Sufficient conditions are provided under which an uncertain system containing parameters varying in any given arbitrary large ranges can be stabilized by a linear static feedback control.