Event-Triggered Variable Structure Control of Nonlinear Switched Descriptor Systems Subjected to Matched/Mismatched Disturbances

This paper investigates the problem of variable structure controller design for a class of continuous nonlinear switched descriptor systems (SDSs) via an event-triggered sampling (ETS) scheme in the presence of matched/mismatched disturbances for the first time. To reduce the usage of energy and computational resources of the system, we propose a novel ETS scheme that avoids destructive Zeno behaviour. Defining a new integral sliding surface, a perturbed nonlinear SDS model is provided for the sliding-mode dynamic. The conditions for the existence of sliding surface and conditions to analyze the regularity, impulse-freeness, and stability of the sliding-mode dynamic with H_∞ performance are derived. To this end, multiple Lyapunov functions and admissible edge-dependent average dwell time (AED-ADT) method are utilized. Based on these conditions, the parameters of the ETS scheme and the sliding surface are co-designed in terms of some linear matrix inequalities. Then, the event-triggered variable structure controller is designed to propel the trajectories of the closed-loop system to the sliding surface. Finally, the effectiveness and superiority of the proposed controller are demonstrated by providing two simulations on an inverted pendulum and a numerical example.