Event-triggered control for discrete-time piecewise affine systems

Abstract

This work addresses the event-triggered control (ETC) of discrete-time piecewise affine systems. We propose a method to design a triggering strategy relying on an implicit representation of piecewise affine systems. Thanks to this implicit representation based on ramp functions, we propose a partition-dependent piecewise quadratic functions to define the trigger criterion and use a piecewise quadratic Lyapunov function candidate to derive conditions to certify the global exponential stability of the origin under the ETC strategy. Since the stability conditions can be expressed as linear matrix inequalities constraints, we propose a convex optimization solution to design the triggering function parameters and to compute the Lyapunov function to ensure the closed-loop stability and a reduction on the control updates. The approach is illustrated by numerical examples.