The problems of filtering and deconvolution are addressed for discrete-time linear systems with deterministic and stochastic uncertainties.

A new lemma is derived which provides the sufficient conditions in terms of LMIs for the guarantee of an upper bound on the induced L_∞$L_{\infty }$ norm of this class of systems.

Two induced L_∞$L_{\infty }$ estimator design methods have been proposed based on quadratic and parameter-dependent stability ideas.