Stability And Stabilization For A Class Of Slowly Switched Positive Systems

Switched positive linear systems(SPLS)are a special class of switched systems.It is composed of a family of continuous-time or discrete-time positive linear systems,and a switching signal governing the switching among them.It should be pointed out that researching on analysis and synthesis of SPLSs is more difficult and challenging than switched systems,since SPLSs combine the complex dynamic behavior of switched systems and the special features of positive systems.In this paper,by employing multiple LyapunovKrasovskii function and the slow switching strategy,the stability and stabilization problems for delayed SPLSs are researched.The main contributes are as follows.Aiming at the problem that the phenomenon of uncertainties extensively exists in the real engineering processes,the problems of robust stability,L1-gain performance and controller design are addressed for switched delay positive systems with polytopic uncertainty.First,by employing mode-dependent average dwell time(MDADT)switching,sufficient conditions of stability are established for the considered system with a class of multiple copositive Lyapunov-Krasovskii function approach.Then,with the aid of the derived results ahead,L1-gain performance is analyzed.Besides,state-feedback controllers are developed to make sure that the corresponding system is stable with L1-gain performance.Finally,we use an example to verify the effectiveness of the results,and prove that compared with ADT,MDADT switching method yields less conservative conditions.The common phenomenon of unstable subsystems of SPLSs is considered.For the discrete-time switched delay positive systems with stable and unstable subsystems,we investigate the problems of stability,stablilization,l1-gain performance analysis.First,by using a class of multiple copositive Lyapunov-Krasovskii function approach,sufficient stability conditions are proposed for the considered system with average dwell time(ADT)switching.Then,based on the stability results,sufficient conditions that guarantee the system to have l1-gain performance are developed.The conditions for the existence of state-feedback controllers are also derived.Finally,we take an example to verify the effectiveness of the results.