Exponential stability for a' class of time-delay systems with uncertainties

Exponential stability conditions based on state observer are discussed for a class of retarded systems. The proof makes use of Lyapunov functions carefully to get the exponential stability conditions and stability degree, and a design method of the observer under this existence condition is developed. The design method is based on the solution of linear matrix inequality and the gains of controller and observer can be designed through the LMIS. The proposed observer is applied to a time-delay uncertain system and simulation results show that the design approach is effective and applicable.