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

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

“…The current results on the finite-time guaranteed cost control problem are focused on integer-order systems, [32][33][34][35][36][37] and few works are devoted to some kinds of fractional-order systems without time delays, [38][39][40][41] not mention to fractional-order systems with time-varying delays. The most frequently used method to solve the problem in these works, [32][33][34][35][36][37][38][39][40][41] the so-called Lyapunov-Krasovskii functional method, cannot be extended to uncertain fractional-order systems with interval time-varying delays easily. It is not easy to construct a suitable Lyapunov-Krasovskii functional for delayed fractional-order systems, and calculate its fractional derivative since the Leibniz rule does not hold for fractional derivatives.…”

“…Remark The current results on the finite‐time guaranteed cost control problem are focused on integer‐order systems, 32‐37 and few works are devoted to some kinds of fractional‐order systems without time delays, 38‐41 not mention to fractional‐order systems with time‐varying delays. The most frequently used method to solve the problem in these works, 32‐41 the so‐called Lyapunov–Krasovskii functional method, cannot be extended to uncertain fractional‐order systems with interval time‐varying delays easily.…”

“…Noted that all the above‐mentioned results focus on integer‐order systems. In FOs, few works can be found in the literature References 38‐41. In particular, the authors in Reference 38 addressed the problem of FTGCC of fractional‐order nonlinear positive switched systems with $$$ D- $$$perturbations via static output feedback controller by proposing linear copositive Lyapunov functions and using the mode‐dependent average dwell time approach.…”

“…In particular, the authors in Reference 38 addressed the problem of FTGCC of fractional‐order nonlinear positive switched systems with $$$ D- $$$perturbations via static output feedback controller by proposing linear copositive Lyapunov functions and using the mode‐dependent average dwell time approach. Liu et al 39 examined the FTGCC of fractional‐order positive switched systems with asynchronous switching and impulsive moments. Shang et al 40 addressed the FTGCC of fractional‐order switched systems with bounded disturbances using multiple Lyapunov functions and the average dwell time approach.…”

“…The major contributions are highlighted below. Distinguished from the works done in References 38‐41, the problem of FTGCC of delayed FOs with convex polytopic uncertainty is proposed for the first time in literature. Based on Laplace transform, we establish new delay‐dependent sufficient conditions for the existence of a guaranteed cost state‐feedback control for the considered system given in terms of LMIs, which can be effectively solved by various computational tools. …”