The Well-Postedness And Robust Stability Of Flexible Beam Systems With Respect To Small Delays In The Feedback Loop

In the paper, we consider the following flexible beam systems with respect to small delays in the feedback loop.with boundary conditionwhere , X[ - , 0] (defined in (2.12)). We prove that it is well-posed when = 0 and that it is robustly stable when 0 < < 1.Firstly, we will formulate the systems as the state linear systems on the suitable Hilbert space X:where z(t) is the state of the systems at time t, u(t) is the input, y(t) is the output, A is the generator of a Co semigroup on X and B, C both are unbounded operators.Since the systems (1) and (3) are equivalent, we only need study the well-poseness with a = 0 and robust stability with 0 < a < 1 of the systems (2).