Analysis and control of the jump modes behavior of 2-D singular systems—Part I: Structural stability

This paper considers the problem of structural stability of 2-D singular systems. Firstly, some properties of structural stability of 2-D general singular systems are presented. Sufficient and necessary conditions for the structural stability of the 2-D singular systems are given. Then, by extending the Lyapunov approach for the structural stability of 1-D continuous singular systems to the discrete case, a generalized Lyapunov equation approach to the analysis of the structural stability of 2-D singular Roesser models (2-D SRM) is proposed. The existence of a solution to the generalized Lyapunov equation gives a sufficient condition for the structural stability of the 2-D SRM.