Dynamic Sliding-Mode Control for Piecewise Affine Systems

This paper investigates the problem of dynamic sliding-mode control through piecewise affine systems (PWAs). An uncertain piecewise affine system is utilized to equivalently represent a general nonlinear system on a compact region around the origin. A piecewise dynamic sliding-mode control law is then constructed for robustly stabilizing the uncertain piecewise affine system and, consequently, for asymptotic stabilization of the corresponding non-aftine continuous-time nonlinear system. The constructed approach holds a favorable feature: it removes some assumptions on the system matrices, thus the developed scheme is more relaxed compared with the published approaches. The simplicity and advantages of the developed scheme is illustrated by a numerical simulation.