Jahnett Uzcategui

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z(n + 1) = A(n)z(n)+ B(n)u(n), n ∈ N∗, z(n) ∈ Z , u(n) ∈ U, where Z , U are Hilbert spaces, A(∙) ∈ l∞(N, L(Z)), B(∙) ∈ l∞(N, L(U, Z)), u ∈ l2(N,U ) and N∗ = N ∪ {0}. Moreover, in the case of exact controllability, the control u ∈ l2(N,U ) steering an initial state z0 to a final state z1 in time n0 is given by the formula u = B n0∗L−1 Bn0 (z1 −Φ(n0, 0)z0),(More)
The main goal of this paper is to prove that the global atractor of the equation ẋ(t) = −kx(t)+β tanh(x(t−r)) is an equilibrium point for any β such that |β| < k. Furthermore, we exhibit numerical evidences that the trivial solution is global asymptotically stable in all the region of the parameters where the equilibrium is local asymptotically stable.
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