Study On Dynamic Properties Of Positive Systems On Time Scales

Positive systems are dynamic systems whose states and outputs remain non-negative under non-negative initial states and non-negative inputs.Due to the wide applications of positive systems in biology,robots and engineering systems,it has attracted attention of many scholars.Additionally,dynamic system theory on time scale is the unification and extension of continuous and discrete systems theory.Recently,some scholars have made preliminary studies on properties of positive systems on time scales,however,the stability and Lp performance analyses of linear systems and dynamic properties of non-linear systems on time scales have not been fully investigated.Therefore,this paper will discuss above problems,the main contents are as follows:We focus on the stability and Lp performance analyses of positive linear systems on time scales,By constructing linear copositive Lyapunov function,uniform stability and uniformly exponential stability conditions are obtained for positive linear time-varying systems on time scales.Then,by using linear programming method,the necessary and sufficient conditions of asymptotic stability are given for positive linear time-invariant sys-tems on time scales,and it is concluded that the asymptotic stability and Lp performance conditions of positive linear systems are independent of time scales.We study the design of Lp state feedback controller and observer.Based on the stability theory,by using the linear programming method,the existence conditions of state feedback controller and observer and specific design method are given.We discuss the positivity and monotonicity of nonlinear systems on time scales.Based on the induction principle,the necessary and sufficient conditions of positive and monotone systems are given for nonlinear systems on time scales,and the relation between nonlinear positive systems and monotone systems are obtained.