Delay-independent exponential stability of recurrent neural networks

Abstract

In this Letter, the authors investigate further the recurrent neural networks model with delays, and give some sufficient criteria ensuring existence, uniqueness and global exponential stability (GES) of the equilibrium point by employing the inequality a ∏ k = 1 m b k q k ⩽ 1 r ∑ k = 1 m q k b k r + 1 r a r ( a ⩾ 0 , b k ⩾ 0 , q k > 0 with ∑ k = 1 m q k = r − 1 , and r > 1 ), constructing a new Lyapunov functional, and applying the homeomorphism theory. These criteria do not require the signal functions are differentiable, bounded and monotone nondecreasing. Thus the criteria obtained have highly important significance in solving optimization problems and reducing the neural computing time. Furthermore, we extend or improve the previously known results.