| Based on advantages and disadvantages of the existing average dwell time and mode-dependent average dwell time strategies,this paper proposes new switching strategies with both advantages,and establishes new stability conclusions for positive switched systems with stable and partially unstable subsystems,the article is divided into three chapters.In chapter 1,we introduce the research status and significance,the preparatory knowledge and the structure of the article.In chapter 2,positive switched systems with two subsystems is taken as the research object in the stability problem.First of all,the stable sufficient condition for the system is derived by the improved mode-dependent average dwell time strategy.And then the stable controller design scheme for non-autonomous case is received by applying the obtained results.In the end,it can be seen from numerical examples that the domain of permissible switching signals achieved by the proposed strategy is bigger than those existing ones,and both the average dwell time and mode-dependent average dwell time strategies can be regarded as some special cases of the theoretical findings in the paper.In chapter 3,positive switched systems with multiple subsystems is investigated.Two new strategies,the weighted average dwell time strategy and the fast weighted average dwell time strategy,are first proposed,and they are used to deal with stable and unstable subsystems of positive switched systems,respectively.Then,based on these two strategies,stability conditions of the system with multiple stable and partially unstable subsystems are further derived.Numerical examples are given to show that the admissible feasible region obtained by the weighted average dwell time strategy covers the ones by the average dwell time strategy and mode-dependent average dwell time strategy under a random switching;those novel strategies can solve defects of the existing literatures on positive systems with unstable subsystems. |
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