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

The problem of stationary robust Linfinity-induced deconvolution filtering for the uncertain continuous-time linear stochastic systems is addressed. The state space model of the system contains state- and input-dependent noise and deterministic parameter uncertainties residing in a given polytope. In the presence of input-dependent noise, we extend the derived lemma in Berman and Shaked (2010) characterizing the induced Linfinity norm by linear matrix inequalities (LMIs), according to which we solve the deconvolution problem in the quadratic framework. By decoupling product terms between the Lyapunov matrix and system matrices, an improved version of the proposed L_infinity-induced norm bound lemma for continuous-time stochastic systems is obtained, which allows us to realize exploit parameter-dependent stability idea in the deconvolution filter design. The theories presented are utilized for sensor fault reconstruction in uncertain linear stochastic systems. The effectiveness and advantages of the proposed design methods are shown via two numerical examples.