Optimal guaranteed cost filtering for uncertain discrete-time linear systems

This paper presents a result on the design of a steady-state robust state estimator for a class of uncertain discrete-time linear systems with normal bounded uncertainty. This result extends the steady state Kalman filter to the case in which the underlying system is uncertain. A procedure is given for the construction of a state estimator which minimizes a bound on the state error covariance. It is shown that this leads to a state estimator which is optimal with respect to a notion of quadratic guaranteed cost state estimation.