Finite Time Delay Switched Stability Studies

There generally exists a phenomenon of pulse or switch in the process of the modernindustrial production. But a simple theory about the impulsive systems or the switchedsystems has its limitation on the modeling and analysis of such a system. Therefore, inrecent years, a model which is called impulsive switched system has been widely concerned bythe control experts. Additionally, most of the literatures focus on the Lyapunov asymptoticstability analysis. However, in a practical application, the usual Lyapunov stability willnot achieve the desired results especially for systems of shorter working hours and fasterresponse. And sometimes it may lead to higher overshoot, slow response and other badefects due to the external disturbance and the uncertain factors. Thus, it is particularlyimportant for the fnite-time stability in many control felds, such as manipulator control,mobile robot control, motor control and space vehicle control etc.This paper is concerned with the problem of fnite-time control for a class of impulsiveswitched systems with time-varying delay. The main results are organized as two parts:1) A fnite-time guaranteed cost controller is designed for the impulsive switched systemswith time-varying delay.The problem of designing a fnite-time guaranteed cost controller is investigated fora kind of impulsive switched systems with time-varying delay. Firstly, the defnitions offnite-time boundedness and fnite-time guaranteed cost control are extended to the impul-sive switched systems. Secondly, based on the average dwell-time technology and multipleLyapunov function method, sufcient conditions ensuring the fnite-time boundedness aredeveloped with no control input. Thereinto, one important consideration is that how to dealwith the impulsive phenomenon occurring at the switching moment in the sense that the de-layed state of the system is time-varying. Thirdly, a fnite-time guaranteed cost controller isdesigned for the system such that the corresponding closed-loop system is fnite-time bound-edness and a guaranteed cost bound is obtained. Further, all the conditions are convertedto solve a set of convex optimization problems. In the end, a numerical example is providedto illustrate the efectiveness of the developed results.2) Robust fnite-time performance analysis for a class of uncertain impulsive switchedsystems with time-varying delay.This study concerns the problem of robust fnite-time performance analysis for a classof uncertain impulsive switched systems with time-varying delay including robust fnite- time guaranteed cost control and robust fnite-time weighted L2-gain analysis. We supposethat the considered uncertainties are norm-bounded. For all admissible uncertainties, somesufcient conditions are given to guarantee the robust fnite-time boundness and the robustfnite-time guaranteed cost control of the closed-loop system with a prescribed weighted L2-gain attenuation level. Then, a fnite-time guaranteed cost controller and a robust fnite-time L2-gain state feedback controller are designed respectively. Meanwhile, a fnite-timeguaranteed cost bound is obtained. Finally, a numerical example is provided to show thefeasibility and validity of the developed results.