Reduced-Order Filter Design for Discrete-Time Systems Corrupted Discrete-Time Systems Corrupted

摘要

THE H1 filtering problem deals with the design of an estimatornable to minimize the L2 gain from the noise signals to thenestimation error. Early formulations and theoretical results for thisnproblem may be found in [1–4], and it represents an alternativenapproach to thewell-knownKalman filter (KF),whichminimizes thenH2 norm of the estimation error. The interest for the H1 filtering isnmainly motivated by robustness reasons, knowing that the KF’snperformance is strongly influenced by the accuracy of the systemnmodeling and the noises statistic properties [1,5]. In the H1 filteringnthere is only a very general assumption about the noise, namely it hasnbounded power.On the other hand, an effectivemethod to handle thenmodeling uncertainties of the system whose states are estimated isnbased on dynamic models with multiplicative noise. Such modelsnhave been introduced four decades ago (see, e.g., [6]) and manyntheoretical results of modern control theory are now available fornthem[7,8]. The systemswithmultiplicative noise are not related onlynwith robustness aspects. Recent research shows that such modelsnnaturally arise in navigation, communications, estimation of targetsnstates, and imagery, to mention only some of their applications innaerospace engineering.