Design of state estimators for linear discrete-time systems with constrained error variance

In this paper, the state estimation problem with constrained error variance for linear discrete-time systems is investigated. To this end, in a first stage, the vector variance equation describing the evolution of the state error variance is established. Then, by applying results from the theory of positively invariant polyhedral sets of discrete-time systems, necessary and sufficient conditions for the state error variance to respect linear constraints are developed. Thus, the determination of the state estimator parameters is reduced to a nonlinear programming problem which can be solved by using various optimization algorithms.