Improved Stability Criteria for Delayed Neural Networks Using a Quadratic Function Negative-Definiteness Approach

A survey of inequality techniques for stability analysis of time‐delay systems

“…However, it may be tedious to identify the coefficients by hand. A simple method has been recently provided to solve this problem, 105 in which the coefficients can be calculated by MATLAB software through formulas, no longer by hand. (…”

“…119 It is necessarily pointed out that since the 𝛼-affine dependent RCCL (like Seuret's RCCL and Zhang's RCCL) is proposed, the further improvement of RCCLs no longer significantly reduces the conservatism of resulting stability conditions. 96,105 Remark 20. Sometimes there is a need to estimate such a matrix term…”

“…Based on previous works, an $$$ \alpha $$$‐polynomial RCCL with infinite series has been developed very recently with a lot of free matrices introduced 119 . It is necessarily pointed out that since the $$$ \alpha $$$‐affine dependent RCCL (like Seuret's RCCL and Zhang's RCCL) is proposed, the further improvement of RCCLs no longer significantly reduces the conservatism of resulting stability conditions 96,105 …”

“…When applying NDLs to obtain a tractable LMI‐based stability condition, one or more of the quadratic coefficients $$$ {a}_2 $$$, $$$ {a}_1 $$$ and $$$ {a}_0 $$$ are required to be explicitly given 53,93,96,104,105 . For instances, when using Chen's NDL, the expression of $$$ {a}_2 $$$ should be got to resolve the inequality (100) while using Zeng's NDL, the expressions of both $$$ {a}_2 $$$ and $$$ {a}_1 $$$ should be known to resolve the inequality (101) because of the fact $$$ \dot{f}\left({h}_t\right)=2{a}_2{h}_t+{a}_1 $$$.…”

“…However, it is not an easy task since these coefficients are usually involved in different complex terms. 72,93,96,104 Fortunately, a simple method has been recently proposed, 105 which not only avoids the tedious handwork but also significantly improves the readability of a resulting stability condition.…”