A Polynomial Approach to Robust Estimation of Uncertain Discrete-Time Systems

The robust estimation problem for uncertain discrete-time systems is treated in this paper considering parametric uncertainties in the polynomial framework. The estimator is the minimiser of a cost function written in a ∈-contaminated form. Uncertainties are not formally modelled. It is shown that, in the present context, the proposed approach can be connected to stochastic modelling of uncertainties. The optimal robust estimator is obtained by computing a spectral factorisation and by solving a single Diophantine equation. An example shows the efficiency of the proposed method.