Stability Analysis And Controller Design Of Linear Switched Positive Systems

Switched positive systems belong to one of the hybrid systems,which have widely applica-tion in quite a few areas,such as network communication,transportation and biology,etc.Due to the interaction between positivity as well as switching features,it is not easy to tackle with such systems.Up till now,not so many conclusions proposed by researchers have emerged,and lots of issues still need to be resolved.The idea of this paper is to utilize the mathematical model of the switched positive system to analyze the stability and design controllers to stabilize the open-loop system in practical application.The main contents are stated as follows:Exponential stability and fault tolerant control for linear time-invariant positive system with controller failure are studied.Through dwell time and mode-dependent average dwell time ap-proach,sufficient conditions of globally uniformly exponential stability are proposed.We treat the mode changing between controller work and failure as a switch.The main idea is using switching behavior to compensate the increment of Lyapunov function produced by controller failure,introducing the multiple linear copositive Lyapunov function method to obtain less con-servative results.By solving the linear programming problem,the switched positive system can be globally uniformly exponential stability under the constraint of dwell time and mode-dependent average dwell time.On this basis,a fault tolerant controller is designed.Stochastic stability of positive Markov jump linear system with fixed dwell time is studied.By constructing an auxiliary system originated from the initial system with state jumps,suffi-cient and necessary conditions of stochastic stability for positive Markov jump linear system are obtained with both exactly known and partially known transition rates.The main idea in the latter case is applying convex combination to convert bilinear programming into linear programming problems.On this basis,multiple piecewise linear copositive Lyapunov function is provided to achieve less conservative results.Then positive Markov jump linear system with state feedback controller is designed to stabilize open-loop system by solving linear programming problems.The exponential stability and L1 gain performance of the positive Markov switched system are investigated.By employing dwell time and mode-dependent average dwell time approach,sufficient conditions of exponential stability for the positive Markov switched system are ac-quired.An auxiliary system is constructed to figure out the problem of Markov chain discon-tinuity caused by the existence of dwell time.In addition,multiple piecewise linear copositive Lyapunov function approach is utilized to analyze L1 gain performance of such systems with external disturbance and L1 controllers are designed afterwards.