Finite-Time Stability Analysis And Synthesis For Distrbuted Parameter Systems

The concept of finite time stability was proposed for the study of the transient performance of a system.Compared with general stability such as asymptotic stability,it's a disparate stability concept of considering the stability performance of a system over a certain time interval.Because of its good robust performance and resistance to disturbance performance,it received widespread attention after it had been proposed.Research results of various systems,such as time-delay systems,switched systems,emerged in endlessly.Results of the combination with other performance index problems such as optimum control,the robust H_? control and Input-Output stability were also common reported.On the basis of predecessors' work,we studied the finite time stability analysis and synthesis problems of distributed parameter systems in this paper.The main innovative contribution of this paper includes the following aspects:?1?Finite-time?FT?stability and stabilization,as well as Input-Output FT stability and stabilization,for distributed parameter systems were studied.The concepts of finite-time stability and Input-Output FT stability were extended to distributed parameter systems:L²-FT stability,W^1,2-FT stability,L²-Input-Output FT stability and W^1,2-Input-Output FT stability.Sufficient conditions of the L²-FT stability,W^1,2-FT stability,L²-Input-Output FT stability and W^1,2-Input-Output FT stability for the distributed parameter systems were established.Based on these sufficient conditions,distributed state feedback controllers which guarantee the closed-loop distributed parameter systems be L²-FT stable,W^1,2-FT stable,L²-Input-Output FT stable and W^1,2-Input-Output FT stable respectively were designed.?2?Finite-time?FT?stability and stabilization,as well as Input-Output finite-time?1-O FT?stability and stabilization,for time-delay distributed parameter systems were studied.Sufficient conditions of the L²-FT stability,W^1,2-FT stability,L²-Input-Output FT stability and W^1,2-Input-Output FT stability for time-delay distributed parameter systems were established.Based on these sufficient conditions,distributed state feedback controllers which guarantee the closed-loop time-delay distributed parameter systems be L²-FT stable,W^1,2-FT stable,L²-Input-Output FT stable and W^1,2-Input-Output FT stable respectively were designed.?3?Finite-time?FT?H_? control problem for time-delay distributed parameter switched systems?DPSSs?was studied.First,finite-time boundedness for time-delay DPSSs was studied.Sufficient conditions of the FT bounded for the time-delay DPSSs are established and a state feedback controller was proposed to guarantee the closed-loop system be FT bounded.Then,FT H_? performance analysis for DPSSs is developed,and a state feedback controller is proposed to guarantee that the closed-loop system be FT bounded with some H_? disturbance attenuation index.