Robust Mixed Performance of Continuous Switched Systems with Time Delay

Abstract

In this paper, the robust mixed H2/H∞ performance analysis of switched time‐delay systems with linear fractional perturbations and distributed delay via a switching signal selection is considered. Some delay‐dependent LMI‐based criteria are proposed to achieve the design of the switching signal. Our approach is guaranteed by the new proposed inequality in recent years. Finally, some numerical examples are illustrated to show the main results.

Mixed performance analysis of continuous switched systems with time‐varying random delay

“…A numerical example was provided to show the proposed results. It is well known that the proposed inequality used in our past result 33 is less conservative than the Wirtinger‐based one in this paper. In the future, we can use this new inequality to improve the proposed criteria in this paper, but more complicated derivations should be overcome.…”

“…If we choose S 1 = − γ 2 Á I, S 2 = I, and S 3 = 0, we can say that the system (5a) is asymptotically mean-square stabilizable with H ∞ performance γ by the switching signal in (3). 32,33 On the other hand, we can say that the system (5a) is asymptotically meansquare stabilizable with passive performance by the switching signal in (3) by choosing S 1 = − γ Á I, γ > 0, S 2 = 0, and S 3 = I .…”

“…If the parameter ℓ 1 is selected as ∞, the disturbance input w should be constrained in L 2 (0, ∞). Then we say that the system is asymptotically mean‐square stabilizable with quadratic performance by the switching signal in (3).Remark If we choose S 1 = − γ 2 ⋅ I , S 2 = I , and S 3 = 0, we can say that the system is asymptotically mean‐square stabilizable with H ∞ performance γ by the switching signal in (3) 32,33 . On the other hand, we can say that the system is asymptotically mean‐square stabilizable with passive performance by the switching signal in (3) by choosing S 1 = − γ ⋅ I , γ > 0, S 2 = 0, and S 3 = I .…”

“…Switching signal design is used to achieve the mixed H 2 /H ∞ or H 2 /passive performance of discrete or continuous switched systems with constant time-delay in. [31][32][33] To the best of the authors' knowledge, there are few results that consider switching signal designs for mixed performance of continuous switched systems with random time-varying delays. 34 Systems with performances of H 2 /H ∞ 34 and H 2 /passivity can be considered as two special cases for the problem under consideration.…”

“…The mixed H 2 / passivity performance is proposed to minimize the upper bound of H 2 performance under a given passive property. Switching signal design is used to achieve the mixed H 2 / H ∞ or H 2 /passive performance of discrete or continuous switched systems with constant time‐delay in 31–33 . To the best of the authors' knowledge, there are few results that consider switching signal designs for mixed performance of continuous switched systems with random time‐varying delays 34 .…”