Stability of nominally stable uncertain singularly perturbed systems with multiple time delays

Abstract: In this paper, the robust asymptotic stability problem for a class of nominally stable uncertain singularly perturbed systems with multiple non-commensurate time delays is considered. A delay-dependent criterion is first proposed in this paper to guarantee robust asymptotic stability of the system under consideration. Based on this result, the range of allowable bounds of the perturbation matrices preserving the closed-loop stability can easily be found. Moreover, a simple criterion is also proposed to guarantee asymptotic stability of the nominal system. Furthermore, a simple estimation of the stability bound c* is proposed such that the nominal system is asymptotically stable for any c E (O,c*). It can be seen that the stability bound proposed in this paper is less conservative than that presented in recent research. Finally, a numerical example is provided to illustrate our main results.