Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

Abstract

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the results.

Novel stability criteria of Cohen–Grossberg neural networks with time‐varying delays

“…Lemma 5 (see Li and Cao [22,30]) If the nonlinear measure satisfies m (F)<0, then F is an injective mapping on . In addition, if = R n , then F is a homeomorphism of R n .…”

Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay

“…As a special class of hybrid systems, switched systems have been extensively investigated, and considerable efforts have been focused on the analysis and design of switched systems [35,20,31,15]. Recently, by integrating the theory of switched systems with Hopfield neural networks, the mathematical model of the switched Hopfield neural networks was introduced to represent some complex nonlinear systems efficiently [14,23].…”

Design of state estimator for uncertain neural networks via the integral-inequality method

“…This motivates the study of the mathematical properties of various neural networks, such as the stability, the attractivity and the oscillation, have become hot research topics and drawn considerable attention. For example, many results on the neural network with constant delay can be found in the work of Marcus [1], Arik [2], Cao [3], Rong [4], Singh [5], and so on; since Ye et al [6] introduced different delays into the Cohen-Grossberg neural networks, many kinds of neural networks with different delays have been extensively investigated [7][8][9][10][29][30][31][32][33].…”