Robust H2/H∞-state estimation with error variance constraints for continuous-time systems with time-varying uncertainties

This paper is concerned with the state estimator design problem for uncertain linear continuous-time systems with H-infinity norm and variance constraints. The uncertainty is assumed to be time-variant and norm-bounded and enters into both the state and measurement matrices. It is also assumed that the uncertainty can be modeled so that it has a structure consisting of a known component and an unknown component. The problem we address is to design a linear state estimator, with a state space equation not dependent on the unknown component of the uncertainty, such that, for all admissible uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from the noise and initial states of the system to error state outputs satisfies the prespecified H-infinity norm upper hound constraint, simultaneously.