Based On Matrix Inequalities, Several Observer Design

In order to solve the contradiction in the state feedback between per-formance which is irreplaceable and the physical nature which can not be achieved, people proposed observer design. On the base of observer design for linear system this paper gives four kinds of system's observer design com-bining matrix inequality and Schur complement theorem. This paper gives a full-dimensional observer design method for a class continuous nonlinear systems which satisfies Lipschitz condition, and transforms it into an opti-mization problem. The latter in this paper derives reduced-order observer design using the given theorem. Then this paper discusses some necessary and sufficient conditions on observer design for the system with uncertainty disturbance and obtains a sufficient condition which is transformed into an optimization problem by L2-gain. In the third section of this paper, this pa-per gives observer design for singular systems by using matrix rank. At last, observer is given for a class of time-delay systems by the method of matrix inequalities. Matrix inequality reduce the storage space and production costs.