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The problem of stationary robust L_infinity-induced deconvolution filteringfor the uncertain continuous-time linear stochastic systems is addressed. Thestate space model of the system contains state- and input-dependent noise anddeterministic parameter uncertainties residing in a given polytope. In thepresence of input-dependent noise, we extend the derived lemma in Berman andShaked (2010) characterizing the induced L_infinity norm by linear matrixinequalities (LMIs), according to which we solve the deconvolution problem inthe quadratic framework. By decoupling product terms between the Lyapunovmatrix and system matrices, an improved version of the proposedL_infinity-induced norm bound lemma for continuous-time stochastic systems isobtained, which allows us to realize exploit parameter-dependent stability ideain the deconvolution filter design. The theories presented are utilized forsensor fault reconstruction in uncertain linear stochastic systems. Theeffectiveness and advantages of the proposed design methods are shown via twonumerical examples.

Robust L_infinity-induced deconvolution filtering for linear stochastic systems and its application to fault reconstruction