H_∞ performance analysis for 2D discrete singular stochastic systems

Abstract

This paper addresses the problem of H_∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an $H_{\mathrm{\infty }}$ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach.

Keywords:

• 2D systems
• singular systems
• stochastic systems
• stability
• $H_{\mathrm{\infty }}$
• strict LMI

Disclosure statement

No potential conflict of interest was reported by the authors.