Design of a robust guaranteed cost observer-based controller for linear uncertain systems

In this paper, a robust guaranteed cost observer-based state feedback controller design problem is studied for a class of linear uncertain systems with norm-bounded uncertainties. Employing the Lyapunov stability theorem, the criteria of robust stabilization are investigated within the framework of linear matrix inequalities (LMI). The feasibility problem of the stabilization criteria is solved using the technique of cone complementary minimization algorithm. Moreover, the minimization of the guaranteed cost is also obtained. Finally, two numeric examples are presented to illustrate the proposed stabilization which provides a considerable improvement.