Regresar

On the controllability of a type of large scale CNN with delays

Abstract:

In this paper we study the approximate controllability of a particular type of large scale CNN (Cellular Neural Network) with delays given by: ẋ = A0x(t) + ∑j=1NAj x(t - h j) + B0u, t ≥ 0, x(0) = r, r ∈ Rn, [ x(θ) = f(θ), θ ∈ [-h, 0), where 0 < h1 < h2 < ... < hN represent the point delays, h = hN, the matrices B0, A0, A(j) ∈ ℒ(Rn), i = 1,2, ... N, the control u belong to L 2([0, τ],Rn) and f ∈ L2([-h, 0]; Rn). Moreover, A0 = diag(A1, ..., A N), B0 = diag(B1, ... BN) and A (j), j = 1, ..., N is an n × n block matrix A(j) = ( 0 ⋯ A1j ⋯ 0 ⋯ A2j ⋯ 0 ⋮ ⋯ ⋮ ⋯ ⋮ 0 ⋯ ANj ⋯ 0) with Ai, Aij, Bi ∈(Rn0), ∀τ > 0.