Optimal robust filtering for linear systems subject to time-varying parameter perturbations

Stochastic linear systems subject to time-varying parameter uncertainties in the state and output matrices are considered. A linear filter is used to estimate a linear combination of the states of the system. When the filter is given, the stabilizing solution of a suitable Riccati equation is shown to yield an upper bound for the covariance of the estimation error. The main problem addressed in the paper is the design of an “optimal robust filter” that minimizes such a covariance bound. Necessary and sufficient conditions for the existence of an optimal robust filter are given in the full order case. The computation of the optimal filter calls for the solution of a Riccati equation that generalizes the standard Riccati equation for the Kalman filtering problem