Novel Global Exponential Stability Criterion for Recurrent Neural Networks with Time-Varying Delay

and Applied Analysis 3 say, there is a parameter sequence (ρ 1 , . . . , ρ K ), which satisfies the following conditions: 0 < ρ 1 τ (t) < ρ2τ (t) < ⋅ ⋅ ⋅ < ρKτ (t) < τ (t) , 0 ≤ ρ i ̇ τ (t) ≤ ρiμ, (9) where ρ i ∈ (0, 1), i = 1, 2, . . . , K, K is positive integer. Utilizing the useful information ofK+1 dynamical subintervals, a novel LKF is constructed, and then a newly LMIbased delay-dependent sufficient condition can be proposed to guarantee the global exponential stability of RNNs with time-varying delay. Theorem 4. The equilibrium point of system (5) with μ < 1 is globally exponentially stable with convergence rate k > 0, if there exists parameter ρ i satisfying 0 < ρ 1 < ⋅ ⋅ ⋅ < ρ K < 1, some positive definite symmetric matrices P, R 1 , R 2 , R 3 , Q i , Z, some positive definite diagonal matrices Λ, X 1 , X 2 , Y 1 and Y 2 , and any matrices M j , where i = 1, 2, . . . , K, j = 1, 2, . . . , 2K + 4, and K is a positive integer, such that the following LMI has feasible solution: [ [ [ [ [ [ [ [ [ [ [ [ [ [