A LMI approach to robust H∞ filtering for discrete-time systems

This paper is concerned with the problem of H_∞-norm and the variance-cost-guaranteed filter for linear discrete-time systems. The system under consideration is subjected to time-variant norm-bounded parameter uncertainties in both the state and output matrices and unknown statistics characteristics but limited power noise. The problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be with a certain bound for all admissible uncertainties and transfer function from disturbances to error state outputs satisfies the prespecified H_∞-norm upper bound constraint, simultaneously. A LMI-based solution for the filter is developed.