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Event-triggered Control of Positive Switched Systems Based on Linear Programming

This paper investigates the problem of event-triggered control for positive switched systems without/with input saturation. A 1-norm based event-triggered mechanism is established for positive switched systems. Using a gain matrix decomposition technique, an event-triggered controller is designed for the systems without input saturation. The saturation term in the saturation systems is transformed into an interval form under the event-triggered mechanism. Then, the upper and lower bound of the saturation systems matrix are obtained. An event-triggered controller is designed to guarantee the positivity of the lower bound closed-loop systems and the stability of the upper bound closed-loop systems in the saturation systems. Meanwhile, a cone attraction domain is constructed and a cone attraction domain gain matrix design approach is proposed. All presented conditions can be formulated into linear programming. Compared with existing results, the event-triggered control is more practical and efficient. Finally, a simulation example is provided to illustrate the validity of the design.