Finite-region boundedness and [formula omitted]-dissipativity of 2-D singular Roesser systems with mixed time-varying delays

Abstract

This paper is concerned with the problems of finite-region boundedness and dissipativity analysis of two-dimensional (2-D) singular Roesser systems with mixed directional time-varying delays. The concepts of singular finite-region boundedness (SFRB), which deduces the property of singular finite-region stability (SFRS) when exogenous disturbance is ignored, and finite-region (Q,S,R)-dissipativity are first proposed. Then, by using an energy function constructed as a weighted 2-D Lyapunov–Krasovskii functional, and by utilizing zero-type free matrix equations, new delay- and time-region-dependent conditions, which guarantee the properties of finite-region stability and dissipativity with respect to a quadratic supplied rate function, are derived. The obtained results are shown to encompass and extend existing works in the literature. The effectiveness of the analysis results is validated by numerical examples.