Stability Analysis And Controllers Design For Switched Positive Systems With Time Delays

Full state is positive and switching system characteristics are switched positive systems,in aircraft control, communication system, medical, engineering and other fields has important theoretical significance and wide application background, to attract many scholars’ attention. At present, scholars are mainly on the stability analysis of the switched positive system, and the research on the performance is not much. Therefore, the author makes an analysis on the performance of switched positive systems. The main research contents are as follows:Firstly, for the linear continuous switched positive systems with state delay and input delay, based on Lyapunov-Krasovskii functional and the average dwell time theory, first of all to make the dual delay linear continuous switched positive systems the sufficient conditions of exponential stability, after given the system state feedback controller design method and ensure the robustH_∞,L₁controller with disturbance rejection capability γ. Next, the corresponding state feedback controller gains are obtained by solving a set of linear programming problems.Secondly, the design of dual linear continuous switched positive system controller is extended to the double linear discrete switched positive systems, and the problem of robust controller design is studied. First of all, the selection of a new linear copositive Lyapunov Krasovskii functional, based on Lyapunov stability theory and the average dwell time theory,conditions for the exponential stability of the system are given and gives the system’s state feedback controller design method. By solving a set of linear programming problems, the corresponding state feedback controller gains are obtained.Finally, in the actual engineering background, the actuator may be inevitable failure,affecting the performance of the system. Therefore, according to the actual system actuator failures that may be occurred by dual delays linear continuous switched positive systems,based on Lyapunov stability theory and the average dwell time theory, first of all to make the dual delays linear continuous switched positive systems the sufficient conditions of exponential stability, after given the system reliable H_∞ and L₁ controller design method and ensure the robust reliable controller can effectively stabilizing the original system and interference suppression capability γ.