Robust H2/H∞ filtering for linear systems with error variance constraints

In this correspondence, we consider the robust H₂/H_∞ filtering problem for linear perturbed systems with steady-state error variance constraints. The purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied. (1) The filtering process is asymptotically stable. (2) The steady-state variance of the estimation error of each state is not more than the individual prespecified value. (3) The transfer function from exogenous noise inputs to error state outputs meets the prespecified H_∞ norm upper bound constraint. We show that in both continuous and discrete-time cases, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like equations/inequalities. We present both the existence conditions and the explicit expression of desired robust filters. An illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach