Guaranteed Cost and Finite-Time Non-fragile Control of Fractional-Order Positive Switched Systems with Asynchronous Switching and Impulsive Moments

Abstract

This paper considers the problem of guaranteed cost and finite-time non-fragile control for a class of fractional-order positive switched systems with asynchronous switching and impulsive moments. Firstly, a novel cost function is presented. The sufficient conditions for the guaranteed cost and finite-time stability of the considered systems are derived via linear programming, using linear co-positive Lyapunov functions, the average dwell time method, and the average impulsive interval approach. Secondly, the finite-time and finite-time non-fragile controllers are designed to ensure that the corresponding closed-loop system is finite-time stable with a certain cost upper bound. Finally, an example of a fractional-order electrical circuit is provided, proving the proposed method’s feasibility and effectiveness.