Variance-constrained multiobjective filtering for uncertain continuous-time stochastic systems

Abstract

In this paper, we consider stochastic linear continuous-time systems subject to parameter uncertainties affecting both system dynamics and noise statistics. A linear filter is used to estimate a linear combination of the states of the system. The problem addressed is the design of a perturbation-independent filter such that, for all admissible parameter perturbations, the following three objectives are simultaneously achieved. Firstly the filtering process is D-stable, that is, the eigenvalues of the filtering matrix are located inside a prespecified disc. Secondly the steady-state variance of the estimation error of each state is not more than the individual prespecified value. Thirdly the transfer function from exogenous noise inputs to error state outputs meets the prespecified H norm upper bound constraint. Therefore, the resulting filtering process will be provided with the expected transient property, steady-state error variance constraint and disturbance rejection behaviour, irrespective of the parameter uncertainties. An effective algebraic matrix inequality approach is developed to solve such a multiobjective H2