Stabilization of fractional switched linear systems via reset control technique

Abstract

This paper deals with the L2 gain stability problem of a class of uncertain fractional switched reset control systems. The stability of the underlying switched linear system with uncertainties and bounded exogenous disturbance is verified via the Lyapunov stability theorem and employing sufficient linear matrix inequalities (LMIs). In this work, the problem of switching between several stabilizing controllers is taken into account, which, all of them are capable of stabilizing the corresponding linear system. Meanwhile, at reset times instants that occur in the jump set, the controller states suddenly jump to the new value based on a proper reset map matrix. Simulation results show that the proposed fractional switched reset controller can attain good robustness performance.