Design of optimal observers for linear time–invariant systems†

Abstract

This paper considers the problem of designing optimal observers for linear time–invariant systems. The optimal criterion introduced here is the time–integral of the mean–square estimation error. A canonical form of the observers is given for simplifying the discussion. A necessary and sufficient condition to this optimal design problem is presented. The result states that the optimal observer is constructed by a reduced (minimal–order) observer with constant gains, which are determined by solving a matrix Riecati equation.