On Stabilization and State Estimation of Impulsive Singularly Perturbed Systems via Sliding Mode Control

Abstract

This paper addresses the problems of designing a nonlinear sliding mode control (SMC) and nonlinear sliding mode observer (SMO) for a class of linear time-invariant (LTI) singularly perturbed systems (SPS) subject to impulsive effects. The continuous states are viewed as an interconnected (or composite) system with two-time scale (slow and fast) subsystems. The main goal is to design a SMC law through the slow reduced order subsystems to achieve closed-loop stability of the full order system. This approach in turn results in lessening some unnecessary sufficient conditions on the fast subsystem. Then, assuming that partial output measurement of the slow subsystem is available, a similar control design is adopted to estimate the states of full order SPS, where a sliding mode modification of a Luenberger observer is used.