Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type
Leonid Berezansky, Josef Diblı́k, Zdeněk Svoboda, Zdenĕk Šmarda · Journal of the Franklin Institute · 2022
Linear neutral vector equations x ˙ ( t ) = A 0 ( t ) x ˙ ( h 0 ( t ) ) + ∑ k = 1 m A k ( t ) x ( h k ( t ) ) + ∫ g ( t ) t P ( t , s ) x ( s ) d s are considered on interval [ 0 , ∞ ) . Here x = ( x 1 , … , x n ) T , m is a positive integer, the entries of matrices A l , l = 0 , … , m , P , and the delays h k , k = 0 , … , m , g are assumed to be Lebesgue measurable functions . New explicit criteria are derived on uniform exponential stability. Comparisons are made and discussed based on an overview of the existing results. An application is presented to local exponential stability of non-autonomous neural network models of neutral type.