The Research On Two Types Of Controlling Problems In The Finite-time

In the analysis and study of the control system,the stability of the system has been a problem that the researchers have been working on.In the previous studies,the most com-prehensive study is the asymptotically stability that is the state of the system under unlimited time.However,in practice,the major concern is the state of the system in a finite-time inter-val,of which the study is quite significant.For this reason,on the basis of previous studies,I researched the stability of two types of systems in a finite-time interval.In this thesis,the way I researched is as follows.In the first chapter,I briefly introduced the background of the stability in a finite-time interval,the research status of domestic and foreign scholars,and the objective of this paper.In the second chapter,I generally summed up the definitions of different types of stability,including the definition of the stability of the singular linear system in a finite-time interval,the definition of the stability of the discrete system in a finite-time interval,and the definition of finite-time boundedness.Besides,in addition to the theorems and properties applied in this thesis,I also introduced the basic knowledge and concepts of the control system.In the third chapter,the robust finite time stability of the singular time-delay system with nonlinear terms is studied.By means of linear matrix inequalities and singular value decomposition delay method,I got a new guaranteed cost controller made sufficient conditions for the robust stability of the closed-loop system in a finite time interval and then by which a numerical example is proposed.Thus the effectiveness of the method is proven.In the fourth chapter,the stability of a class of linear discrete-time systems in a finite time interval and H_?control have been investigated,subject to interval time-varying delay and norm-bounded disturbances.Based on the LMI approach,by means of constructing a set of improved Lyapunov-like function,the sufficient conditions for the robust finite-time stability of the system under no control terms are presented,and then through the design of feedback state processor extended the results further,making the closed-loop system of the original system finite-time bounded.Meanwhile,It also ensures that the closed-loop system satisfies H_?performance.In the end,two numerical examples are given to prove that the theorem is valid and reasonable.In the fifth chapter,we summarize the current research work,and discuss the future work.