Local Perturbation Limits of the Discrete Matrix Inequality Linear Quadratic Regulator Task for Differential-algebraic Systems

The theory of optimal control is connected with keeping a dynamical system at minimum cost. The situation where the system behavior is depicted by a set of linear differential equations and the cost is described by a quadratic function is considered to be the linear quadratic (LQ) task. The discussed regulation task can be clearly accomplished by the solutions Q, Y of a system of linear matrix inequalities (LMIs). This paper is devoted to conditioning of the discrete-time LMI based linear quadratic regulator task for differential-algebraic (DAE) systems. To determine the local perturbation limits of the matrix inequalities we introduce an appropriate term on the right, which is somehow perturbed. Based on the perturbation analysis we obtain narrow local perturbation limits for the LMIs’ solutions to the LQR task. The results are illustrated by an example.