Robust Filtering for Linear Time-Invariant Continuous Systems

The problem of robust filtering for linear time-invariant (LTI) continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations, and then in the state-space domain. The basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv-contaminated model. The general solution to the problem is given in the transfer function representation while, in the polynomial framework, the causal estimator is obtained by means of a spectral factorization and a Diophantine equation. The state-space realization of the causal estimator is discussed. Examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty.