A kind of robust controller for uncertain linear system LQ tracking problem

In this paper, the problem of linear quadratic tracking with infinite time-invariant is discussed. The description of matching uncertain linear system is presented and the error equation of the system is established, which can be considered as the general error dynamic system (GEDS). Hence, the tracking problem is transformed into stabilization issue. A kind of robust linear quadratic tracking controller is designed by solving a Riccati inequation which contains the uncertain information with the LMI method. By Lyapnov function, it can be proven that the controller guarantee all signals in the closed loop system robust stable. In addition, a simulation example is provided, which illustrates that the proposed controller results in robust performances to the model perturbation. The effectiveness of the designed control law is verified. The work done in the paper also improves the controller design method for linear quadratic tracking problem.