Abstract-This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability.
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.
In this paper, the so-called full block Sprocedure is applied to propose a general methodology that enables the derivation of LMI stability conditions for a quite general class of multidimensional linear systems, namely those described by hybrid Roesser models.
This paper deals with the stability and stabilization of 2D singular systems described by a Roesser model. The proposed results are presented in terms of a strict Linear Matrix Inequality (LMI), which makes possible to elaborate a new sufficient admissibility condition. Based on this condition the design of a state feedback controller is also treated, deriving a sufficient condition for the admissibility of the closed loop system. A numerical example is given at the end of the paper to illustrate the effectiveness of the proposed methodology.
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