Finite-time Stability And Filtering For Impulsive System

Abstract Impulsive system is a hybrid dynamic system which combines contin-uous process and jumping in the state. It is widely applied in the areas of physics, pharmacodynamic, ecosystem, automatic control etc. In actual engineering, for those systems whose working time is short (such as missile system, communication network system, robot control system, etc.), people are concerned that systems should satisfy certain transient performance requirements(such as meeting certain deviation range of the system trajectory for balance requirements). Since the finite-time stability(FTS) well depicts the transient performance of the system, it has received more and more attentions from scholars and has achieved fruitful results. On the other hand, in the fields of the communication, signal processing and con-trol, how to filter noises from the signal polluted by noises, eliminate the influence of noises, and strive for the unknown real signal or estimate system states is also one of a hot topics in the control field. Because of the increasing attention to the finite-time stability problem and the wide application of H?, filter, several types of impulse systems'finite-time stability and H?filtering problems are studied in this paper, using the Lyapunov function and linear matrix inequality(LMI) methods to establish some sufficient conditions.The present paper is divided into five chapters.The first chapter overviews some basic knowledge about stability, finite-time stability, H?filtering and finite-time filtering, which are preparatory for the latter chapters.The second chapter firstly introduces the finite-time filtering problem of discrete-time linear impulse system researched by Xu J. et al, then shows that the conclusions are not correct by using a numerical example and simulation, finally, finds out the reasons using theoretical analysis and presents correct conclusions. Since the vari-ables are coupled in this conclusion, it cannot be solved by using Matlab Toolbox directly. In order to avoid the above situation, two relatively practical results are given. Then similar results for the finite-time filtering problem of the continuous-time linear impulse system are established. Numerical simulation shows that the filtering method is feasible and effective.The definitions for finite-time stability and finite-time filtering problem of the discrete-time and continuous-time singular linear impulse system are given in third chapter, respectively. Sufficient conditions and the design methods of filter, which meet the finite-time stability the H?performance requirements, are given for the singular impulsive system by using Lyapunov method. Numerical simulation shows the feasibility and effectiveness of the conclusion.Taking advantage of Lyapunov method, the finite-time stability and L2-gain problems for linear time-varying singular impulse system are investigated in forth chapter. Sufficient conditions, which can ensure that singular system is finite-time stable and can satisfies L2-gain performance, are given with Lyapunov method. Compared with the constant disturbance, systems with time-varying disturbance can reflect the real world, so the finite-time stability problem for the impulse sin-gular systems with time-varying disturbance is studied. Based on the different characteristics of disturbances, corresponding conclusions are given, respectively. If the disturbance is a constant, the conservatism of the conclusion is reduced by using of the slack variable. Numerical examples show that the conclusions is feasible and this method has a larger scope.The finite-time filtering problem for the discrete-time and continuous-time im-pulses piecewise affine system is studied in fifth chapter, respectively. Some sufficient conditions for the filter error system that is finite-time stable and meets H?per-formance requirements are given by using of the method of Lyapunov function and linear matrix inequality; And sufficient conditions for the solvability of the finite-time filtering problem and designing methods of the filter are also given. Finally, the numerical simulation shows the feasibility of this method.