Guaranteed cost control of robot manipulator with prescribed degree of stability

In this paper, we propose a robust controller design method for a linear time invariant system which combines two methods. The first one is referred as guaranteed cost control, that is one kind of a robust design method for the system with structured uncertainty. It gives a robust stable feedback law, which guarantees an existence of the upper bound for the effect of a perturbation. The second one is called prescribed degree of stability. For a nominal system, by a transformation of a state and input vector, it can relocate all the poles of the closed-loop system to leftward in the complex plane, after a design procedure based on the cost minimization like the linear quadratic regulator. Thus, our proposed method is able to design a robust stable controller, and it can also adjust the system characteristics on the complex plane. At last, we show the validity of our proposed method through the numerical example.