Exponential stability conditions for 2D continuous state-delayed systems

Abstract

In this paper, we define the notion of exponential stability for continuous D Roesser models with state delays and develop, using the Lyapunov approach, new tractable conditions (LMI type) to check the exponential stability of 2D linear delayed systems. Illustrative examples are introduced to prove the efficiency of the proposed criteria.

Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability

“…This is what has been recently proposed in the continuous case [24]. It is however not sufficient for us, because with this definition, it is not guaranteed that exponential stability will imply asymptotic stability in the way we want to define it.…”

Lyapunov theory for continuous 2D systems with variable delays: Application to asymptotic and exponential stability

“…Remark 4: In this paper, similar to [11], a sufficient condition is provided showing that the system under consideration is stable if there exist a vector Lyapunov function satisfying certain positivity conditions (7a)-(7b) together with its divergence along the system trajectories (8). The main difference with the condition presented in [11,Lemma 1] lies in the upper bounds of V h and V v .…”

“…Remark 1: Note that this definition is slightly different compared to the one given in [8], in order to be coherent with the definition of asymptotic stability for 2D systems: if the system is exponentially stable it implies the asymptotic stability as lim…”

“…This paper focuses on continuous 2D systems with delays. The literature on the stability of 2D systems with delays is scarce: we can just cite [1], [2], [8], [10], [11]. However the Lyapunov techniques used in these works are based on a similarity assumption between 1D and 2D systems which could be false.…”

H∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

“…The stability and stabilisation problems of 2-D discrete systems have been studied by many researchers (see Bachelier, Paszke, Yeganefar, & Mehdi, 2013;Bouagada & Dooren, 2013;Du & Xie, 1999;Du & Xie, 2002;Hinamoto, 1997;Hmamed, 1997;Li, Ho, & Chow, 2005;Paszke, Lam, Gałkowski, Xu, & Lin, 2004). Recently, some results on stability and stabilisation of 2-D continuous systems have also been obtained (see Benhayoun, Mesquine & Benzaouia, 2013;Benzaouia, Benhayoun & Tadeo, 2011;Galkowski, Paszke, Sulikowski, Rogers, & Owens, 2002;Ghamgui, Yeganefar, Bachelier, & Mehdi, 2011;Hmamed, Mesquine, Tadeo, Benhayoun, & Benzaouia, 2010).…”