Functionals with sign-definite derivative for the stabilization of delay systems (Q731535)

From the summary: ``We present new conditions for the uniform asymptotic stability of equilibria in delay systems. These conditions are based on Lyapunov functionals that have negative definite derivatives along the trajectories of the system only on some part of the phase space. By using these conditions, we establish new optimal stabilization tests, which admit the use of a performance functional whose weight functional is not negative definite on the entire phase space. We introduce a new notion of smallness for perturbations in delay systems and present stabilization tests by the first approximation.''