Research On Finite Time Robust Filtering Problems For Uncertain Systems

Signal filtering is the core problem in cybernetics and information theory,since the signal is inevitably polluted by noise signal during transmission and detection.In order to obtain the required signal,it is necessary to design the corresponding filter for the controlled system.However,the actual application of the system can not be used to describe the linear model,the structural parameters are not fixed,which we call uncertain systems.Uncertain systems are more ignificant than linear systems,and the filtering problem of uncertain systems has been paid more and more attention.Since 1980 s,scholars have developed robust filtering theory and achieved a lot of results.In many fields such as aviation,aerospace,chemical and so on,the state of the controlled system needs to be switched frequently,which poses a higher demand for the transient performance of the system.In this case,the concept of finite time stability is presented.Unlike progressive stabilization,finite time stability requires that the system state variables remain within the specified range for a given time interval.If an additional interfering signal is introduced into the system,the finite-time stability problem becomes a finite time bounded problem.With the development of robust filtering theory,the finite time filtering theory has been paid attention in recent years.However,scholars' research are more about linear switching systems,there are few research results on the finite time filtering problem for uncertain systems.In this thesis,we mainly study the finite-time filtering problem for uncertain systems by using Lyapunov stability theory.This thesis focuses on uncertain systems which can be described by convex polyhedron.Firstly,the su cient conditions for the finite-time bounded filtering problem of uncertain systems are given by constructing a quadratic Lyapunov function.Then,the decision matrix is transformed into a linear matrix inequality group by means of contract transformation and Schur complement transformation.In this way,it becomes a feasible solution to the linear matrix inequality group.Furthermore,a similar method is used to introduce the H_? filter in the uncertain systems to study the finite-time issue of the uncertain system.Su cient conditions for the finite-time boundedness of the error system are given,and the design method of the filter is given.Finally,the solution and simulation of the parameter-dependent uncertain systems and state-dependent uncertain systems respectively are presented.Introduce state delay in the above uncertain system.Firstly,the Lyapunov-Krasovskii function is used to construct the decision matrix of finite time bounded filtering problem for uncertain systems with time delay.Similarly,the decision matrix decoupling is linearized into a linear matrix inequality group,and the solution problem of the filter becomes a feasible solution of the linear matrix inequality group.Furthermore,we consider the finite time bounedeness H_? filter problem of the time-delay uncertain system,the design method of the filter is obtained.Finally,it is applied to an instance of an indeterminate system for solving and simulating.