Adaptive Sliding Mode Control for Nonlinear Impulsive Time-Delay Hybrid Systems

This article investigates the adaptive sliding mode control (ASMC) for a class of nonlinear impulsive hybrid systems with time-varying delay, adopting a creative approach that emphasizes the switching perspective. When both impulse and sliding mode control are involved in the time-delay system, ensuring the continuity of the sliding mode function (SMF) and achieving the reachability of system states become crucial challenges that need to be addressed. In view of this, a novel impulse-based SMF is developed such that the impulsive effect can be avoided on sliding surface, and the difficulty of its continuity is also settled at impulsive instants. By using the state augmented approach, the delay-dependent Lyapunov function with switched systems is formulated to guarantee robust stability of the given sliding mode dynamics. Meanwhile, the designed ASMC law is derived to achieve the finite reachability of switching surface for system states. It is shown that the proposed ASMC law offers a high degree of freedom for adjusting the constants in nonlinear assumptions. Finally, comparative studies are conducted to validate the theoretical results and demonstrate their practical applicability.