Abstract
This paper focuses on the design of <i>l</i><sub>2</sub> gain controller for discrete time switching systems with dwell time (DT) switching. So far, the quantitative relationship between <i>l</i><sub>2</sub> gain stability and dwell time is one of the unsolved problems in the field of switching systems. Different from previous studies, a novel dwell time dependent Lyapunov function (DTDLF) is proposed in this paper for the first time to obtain a less conservative stability criterion. The innovation of this Lyapunov function lies in that it is no longer built by the traditional two-step controller design method, but combines the two design tasks of controller and switching law into one framework, in which solving linear matrix inequalities (LMIs) involves only one step. Compared with the two-step design scheme, this method greatly simplifies the design process. Based on the resident time dependent Lyapunov function and the resident time switching strategy, a dwell time dependent (DTD) H<sub>∞</sub> controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed H<sub>∞</sub> performance index. Finally, a numerical example is given to verify the validity of the proposed design method. The simulation results show that the proposed design method can guarantee a shorter resident time limit and a smaller error result.
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