Consider the first-order linear delay differential equation x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, and the second-order linear delay equation x′′(t) + p(t)x(τ(t)) = 0, t ≥ t0, where p and τ are continuous functions on [t0,∞), p(t) > 0, τ(t) is nondecreasing, τ(t) ≤ t for t ≥ t0 and limt→∞ τ(t) = ∞. Several oscillation criteria are presented for the first-order equation when

This paper is has addressed the Single Flexible Link Robot. The dynamical model is derived using Euler-Lagrange equation and then a proper controller is designed to suppress a  vibration based-on Input-Shaping (IS) method. But, IS control method is an open loop strategy. Due to the weakness of open loop control systems, a closed loop IS control system is proposed. The achieved closed loop c...