Event-triggered constrained control of positive systems with input saturation

This paper addresses the problem of event-triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event-triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed-loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event-triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event-triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.