Integral sliding mode control for singularly perturbed systems with matched disturbances

Abstract

This paper presents a novel integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with matched disturbances. Firstly, a linear state feedback control law for the fast subsystem of SPS is designed, and the slow subsystem can be obtained. Secondly, an ISMC incorporating the disturbance estimate provided by a disturbance observer is designed. In order to attenuate matched disturbances, the Lyapunov function is employed to determine the gain of ISMC by solving a linear matrix inequality (LMI). As a result, the closed-loop slow subsystem under the ISMC is exponentially stable, and the full-order SPSs are exponentially stable under the composite control law. Finally, the effectiveness and advantages of the proposed method are demonstrated by simulations.