The robust D-stability analysis of uncertain discrete-delay descriptor systems via genetic algorithms

Abstract

In this paper, work concerning robust D-stability analysis is considered for discrete descriptor systems with structured uncertainties and multiple time delays. A genetic algorithm is used to make the stability test of the main result more efficient. A delay-dependent robust D-stability criterion is proposed to ensure that all poles of the discrete multiple time-delay descriptor systems subject to uncertainties are located within a disk contained in the unit circle. It will be seen that the system considered in this paper is more general and the proposed robust D-stability criterion is less conservative and easier to check than those presented in recent research. Moreover, a delay-dependent criterion is derived to guarantee that the system is regular, impulse-free, and D-stable. Since the boundary test occurs during the check of the criteria, a genetic algorithm is used to make it more precise. Finally, an example is introduced to illustrate our main results.