Optimal observer design for uncertain linear dynamical systems with unknown inputs

This paper deals with the problem of optimal state estimation of uncertain linear systems with unknown inputs. The system under consideration is subjected to unknown inputs and bounded parameter uncertainties in both state-input and measurement matrices. The proposed method uses ellipsoidal set-theoretic approach, and the optimal observer design is to minimize the bound of the ellipsoid of the estimation error and to be insensitive to unknown inputs. At first we employ a regular, but not unique, transformation which leads to a stochastic differential algebraic equations. Sufficient conditions for the optimal design problem are established.