Perturbation Analysis of the LMI-based Continuous-time Linear Quadratic Regulator Problem for Descriptor Systems

The Linear Quadratic Regulator Problem (LQR) is applied in order to compute a control law that can achieve stability of the closed-loop system and predefined performance by minimizing a given cost function. In this paper we present an approach to perform perturbation analysis of linear quadratic regulator problem for continuous-time descriptor systems. The considered control problem is based on solving LMIs (Linear Matrix Inequalities) and applying Lyapunov functions. The paper is aimed at obtaining linear perturbation bounds for the continuous-time linear quadratic regulator problem for descriptor systems. The computed perturbation bounds can be used to investigate the effect of perturbations in system and controller on feasibility and performance of the considered control problem. A numerical example is also studied in the paper.