Abstract: For the linear quadratic(LQ) optimal control system, a method is proposed to choose the suitable weighting matrices which make the system have desired closed loop poles. The weighting matrices can be regulated by transformation matrices which are related to the desired system poles. So the LQ system acquires the desired dynamic quality. These designs are based on the system normal model. When perturbations occur, the stability and desired performance of the system are affected severely. So it is very important to obtain the allowable stable perturbation bounds for analysis and design of the system. In this paper, a robustness measure bound is introduced for the state feedback system, and the stable bounds of the closed loop system in the presence of perturbations are derived. The stable bounds are obtained for allowable nonlinear time varying perturbation. In particular, for linear perturbations the stable bounds are also derived. A numerical example is finally included to demonstrate the proposed procedure.

Key words: optima l contr ol, closed loop poles, pertur bat ion bounds