Passivity-Based Sliding Mode Control for Lur'e Singularly Perturbed Time-Delay Systems with Input Nonlinearity

This paper addresses the passivity-based sliding mode control (SMC) for Lur'e singularly perturbed time-delay systems with input nonlinearity. First, a novel epsilon-dependent sliding mode surface is designed such that resulting sliding mode dynamics is still a singularly perturbed system. Based on this, a SMC law is designed to guarantee that the system state can be driven onto the specified sliding mode surface in a finite time and stays there for all future time. Then, delay-dependent and delay-independent sufficient conditions are proposed such that the sliding mode dynamics is passive and asymptotically stable. The criteria presented are both independent of the small parameter and the upper bound for the passivity can be obtained in a workable computation way. Finally, the validity of the developed methods is illustrated by three numerical examples.