First Order Perturbation Bounds of the Discrete-Time LMI-Based H∞ Quadratic Stability Problem for Descriptor Systems

In this paper we propose an approach to obtain first order perturbation bounds for the discrete-time Linear Matrix Inequalities (LMI) based H∞ quadratic stability problem for descriptor systems. Applying the considered approach we are able to compute tight first order perturbation bounds for the LMIs’ solutions to the H∞ quadratic stability problem for discrete-time descriptor systems. In the paper we present an approach to compute the estimates of the individual condition numbers of the considered LMIs. To illustrate the performance and applicability of the results obtained we present a numerical example