Stability Analysis And Control Synthesis Of Positive Differential-difference Equations

Positive systems have attracted researchers' attentions due to their applications in fields of communication engineering,biochemistry,social sciences,economics and so on.And differential-difference equations(CDDEs)can represent a variety of time-delay systems,have attracted researchers' great interest.This paper focus on stability and control problem of positive delay differential-difference equations.The main research results were showed as following:Firstly,the problems of stabilization of positive CDDEs with unbounded time-varying delays are studied.By constructing estimates of the solutions,we get the sufficient and necessary condition on asymptotical stability of positive CDDEs with unbounded time-varying delays.Then,by this sufficient and necessary condition,the problem of stabilization for positive CDDEs with unbounded time-varying delays is researched.Based on static output feedback controllers and static state feedback controllers,we ensure that the corresponding close-loop systems are positive systems and asymptotically stable,respectively.Finally,simulation examples are given to verify the correctness of the conclusions.Secondly,for positive CDDEs with bounded time-varying delay,the problems of finitetime stability and finite-time control are researched.First,the definition of finite-time stability of is extended to positive CDDEs with bounded time-varying delay for the first time.Then,by constructing estimates of the solution,a sufficient condition is provided to ensure the finitetime stability of positive CDDEs with bounded time-varying delay.By this result,we point out that static output feedback controller and static state feedback controller are designed to ensure the corresponding closed-loop systems are positive and finite-time stable.And,the delay is not assumed to be differentiable.So,our results are more general.Finally,simulation examples are given to verify the correctness of the conclusions.Thirdly,the problems of finite-time boundedness and finite-time control of positive CDDEs with bounded time-varying delay are investigated.First,the definition of finite-time boundedness is extended to the positive CDDEs with bounded time-varying delay.By coordinate transformation and constructing estimates of the solution,the finite-time boundedness of positive CDDEs with bounded time-varying delay is considered,with a sufficient condition be provided.Then,by this result,the static output-feedback controller and the static state feedback controller are designed to ensure the positivity and finite-time boundedness of the corresponding closed-loop systems.Then,using the method of linear programming,we provide an algorithm to solve feedback gain matrix.Finally,simulation examples are given to verify the correctness of the conclusions.