On Designing Filters With Circular Pole and Error Variance Constraints

In this paper, we deal with the problem of designing a filter for discrete-time systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for each state is not more than the individual prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an algebraic matrix inequality approach. The proposed design algorithm is illustrated by a numerical example.