Lyapunov theory for 2D Roesser models: application to the asymptotic and exponential stability
نویسندگان
چکیده
This paper deals with a general class of discrete 2D systems based on the Roesser model. We first discuss the existing definitions of (Lyapunov) stability in the area of multidimensional systems and provide strong incentives to adopt new definitions in order to be coherent with the ones usually adopted in the 1D case. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability. Note that the theory can be applied both for linear and non linear systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability for 2D systems. keywords: nD systems, Lyapunov stability, discrete systems.
منابع مشابه
Stability analysis of 2D Roesser systems via vector Lyapunov functions ?
The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov’s method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explic...
متن کاملGlobal Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays
In this paper, a bidirectional ring network with three cells and different time delays is presented. To propose this model which is a good extension of three-unit neural networks, coupled cell network theory and neural network theory are applied. In this model, every cell has self-connections without delay but different time delays are assumed in other connections. A suitable Lyapun...
متن کاملBulletin of the Polish Academy of Sciences
Abstract. A new class of fractional 2D Lyapunov systems described by the Roesser models is introduced. Necessary and sufficient conditions for the positivity and asymptotic stability of the new class of systems are established. It is shown that the checking of the asymptotic stability of positive 2D fractional Lyapunov systems can be reduced to testing the asymptotic stability of corresponding ...
متن کاملFuzzy Lyapunov stability and exponential stability in control systems
Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...
متن کاملAsymptotic stability of positive 2D linear systems with delays
Abstract. New necessary and sufficient conditions for the asymptotic stability of positive 2D linear systems with delays described by the general model, Fornasini-Marchesini models and Roesser model are established. It is shown that checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to the checking of the asymptotic stability of corresponding positive ...
متن کامل