Robust H∞ filter design with variance constraints and parabolic pole assignment

In this letter, we consider a multiobjective filtering problem for uncertain linear continuous time-invariant systems subject to error variance constraints. A linear filter is used to estimate a linear combination of the system states. The problem addressed is the design of a filter such that, for all admissible parameter uncertainties, the following three objectives are simultaneously achieved: 1) the filtering process is P-stable, i.e., the poles of the filtering matrix are located inside a parabolic region; 2) the steady-state variance of the estimation error of each state is not more than the individual prespecified value; and 3) the transfer function from exogenous noise inputs to error state outputs meets the prespecified H_∞ norm upper-bound constraint. An effective algebraic matrix inequality approach is developed to derive both the existence conditions and the explicit expression of the desired filters. An illustrative example is used to demonstrate the usefulness of the proposed design approach.