Abstract: Regarding a class of linear systems with normbounded uncertainty and external disturbancey, it advances a method of designing robust guaranteed cost controllers for linear systems with uncertainty, based on observers. Sufficient conditions for the existence of the controllers were obtained via the use of state transformation and Lyapunov stability theorem. The designed controllers can not only guarantee the stability of the closed-loop system, but also ensure that the closed-loop system has a certain linear two-type energy index and H_∞ performance index. The effectiveness of the method has been verified by simulation.

Key words: observer; guaranteed cost controller; uncertainty; linear matrix inequality