A Linear Matrix Inequality Approach To Design Filter

The state filter problem is one of the fields that have been attracted muchattention in the control theory and in the practice application. The filter foruncertain system is caused more and more attention in the last few years.The uncertainties can be described as parameter disturbs. The aim of filter isto eliminate the disturbance from the disturbed so that to get the usefulinformation. Namely the filter value of useful message is got by dealingwith a series of measure date with error. The change of the uncertainparameters in the practice maybe great , and this requires the filter has goodrobust performance similarly.The class design of H∞filtering base on algebraic Riccatti equation(ARE) approach. The ARE approach involve a conversion of the robust H∞filtering problem into a "scaled"H∞filtering problem. This is done byconverting of the norm-bounded uncertainty into some scaling parameters.The conversion used there significantly simplifies the robust H∞filteringproblem and make it possible to use the standard H∞filtering result.However, the introduction of the scaling parameters makes the resulting"scaled"ARE's difficult to solve. Indeed, these scaling parameters enter theARE's nonlinearly. Further, the norm-bounded uncertainty assumption issomewhat conservation in many applications. These defections limited inthe quality and application of the robust H∞filtering base on ARE's.The main work of the paper is to using linear Matrix inequality to robustH_∞filtering. Base on H∞norm , we consider a general class of uncertainlinear systems described by the so-called integral quadratic constraints(IQC's). The main work of the paper is to show that the robust H∞filtering problem can be solved using linear matrix inequality (LMI)techniques. The system considered an energy bounded exogenous noiseinput . The design approach to robust H∞filtering for linear systemssolved via three linear matrix inequalities (LMIs) is presened . this approachis overcome the defects based on algebraic Riccati equations(ARE's) .Dueto recent advancement in convex optimization , efficient algorithms existfor solving LMI's. The paper deals with both continuous and discretecontinuous-time uncertain linear system. The whole dissertation includes the following four contains:(1)Overview of the preliminariesIn this section, we briefly review the standard H∞filtering approachesfor linear system without model uncertainty. We get the structure and theapply object of H∞filter. Presentation several design methods for H∞filter generally and comparing the merits and demerits of several designmethods. Given the basic anamnesis and a few of achievement that thegrand old man got. It is shown how a complex system can be described ,using linear matrix inequality (LMI) techniques and integral quadraticconstrains(IQC's) for its elementary components and defined.(2) H∞filter design with basic method First aiming at linear system, we use H∞norm as index to educe thelinear matrix inequality expression which decide whether the H∞filterexists or not. we can judge whether the linear matrix inequality havesolution by using existing tool box in Matlab. Then we can judge whetherthe robust H∞filter exists. If the robust H∞filter exists, we can optimizethe H∞filter index to get the optimal robust H∞filter.(3) H∞filter design with integral quadratic constraints In this part, apart from an energy bounded exogenous noise input , thesystem allowed to have uncertainties described by the so-called integralquadratic constraints. Based on the system , given a linear matrix inequalityapproach to robust H∞filter. The problem of robust H∞filter contains twoaspects: H∞filter analysis and H∞filter synthesis. We apply the so-callS-procedure to deal with the IQC's and provide solutions to the robust H∞filter problem, convert the H∞filter problem to H∞controlproblem.Based on H∞norm theory, sufficient conditions for stability of...