Stability Analysis And Synthesis Of Switched Positive Systems

Switched positive systems are a special kind of hybrid systems which have a extensive application in biology,medical science,network communication and so on.This kind of system is composed of a class of positive subsystems and a switching law.Because of the interaction of positive constraint and complex dynamics,it is more difficult to study switched positive systems.There are few result on the problem of switched positive systems and many issues of this kind of systems require to be solved.This paper investigates the stability analysis and synthesis of switched positive systems,the main contents are summarized as follows:The globally uniformly exponential stabilization problem of continuous-time and discretetime switched positive systems with both unstable and stable subsystems under mode-dependent average dwell time is investigated.By using the multiple piecewise-continuous linear copositive Lyapunov function,stability criteria are obtained with a switching strategy where fast switching and slow switching are applied to unstable and stable subsystems respectively.The obtained results are proved to have higher bounds on mode-dependent average dwell time of unstable subsystems and lower bounds on mode-dependent average dwell time of stable subsystems compared with the existing results in the literature.State-feedback controllers are also designed for the system with uncontrollable and controllable subsystems.The globally uniformly asymptotically stabilization problem of discrete-time switched positive T-S fuzzy systems with both unstable and stable subsystems under mode-dependent average dwell time is studied.State-feedback controllers are also designed for the system with uncontrollable and controllable subsystems.By using a kind of special copositive Lyapunov function,stability criteria are obtained and the obtained results are less conservative compared with the existing results in the literature.The finite-time bounded of linear switched positive time-varying systems under minimum dwell time is discussed.By using the time-varying copositive Lyapunov function,finite-time bounded criteria are developed.And a algorithm is given to design the switching rule.The results can be obtained by solving a linear programming problem with discrete sample time instants and this method can reduce the computational complexity compared with the existing results.The proposed method can also be used to solve the problem of L1 finite-time bounded of this kind of systems.