The purpose of this thesis is to develop designing methods of robust LQR/LQG controllers for time-varying systems with real parametric uncertainties. Controller design that meets desired performance and robust specifications is one of the most important unsolved problems in control engineering. We propose a new framework to solve these problems using Linear Matrix Inequalities (LMIs) which have gained much attention in recent years, for their computational tractability and usefulness in control engineering. In Robust LQR case, the formulation of LMI based problem is straight forward and we can say that the obtained solution is the global optimum. because the transformed problem is a convex problem. In Robust LQG case, the formulation is difficult because the objective function and the constraint are all nonlinear, moreover these are not a treatable form by LMI. We propose a sequential solving method which consists of a block-diagonal approach and a full-block approach. Block-diagonal approach gives a conservative solution and it is used as an initial guess for a full-block approach. In full-block approach, LMI and Lyapunov equation are solved sequentially in iterative manner. Because this algorithm must be solved iteratively, the obtained solution may not be the global optimum.
