摘要：The Linear Quadratic Regulator (LQR) problem is used to obtain a control law that can ensure stability of the closed-loop system, desired performance and minimizes a predefined cost function. The considered control problem can be implicitly realized using the solutions Q, Y of a system of Linear Matrix Inequalities (LMIs). In this paper we perform linear perturbation analysis for the discrete-time LMI based linear quadratic regulator problem. The problem of performing sensitivity analysis of the perturbed matrix inequalities is considered similarly to perturbed matrix equations, after introducing a slightly perturbed suitable right hand part. The proposed approach allows to obtain tight linear perturbation bounds for the LMIs’ solutions to the linear quadratic regulator problem. In the paper numerical examples are also presented.
关键词：Perturbation analysis; Linear Quadratic Regulator Problem; LMI based;synthesis; Linear systems.
