STABILIZING INPUTS FOR IMPLICIT FUNCTIONAL DIFFERENTIAL EQUATIONS OF THE NEUTRAL TYPE WITH UNKNOWN TIME-VARYING DELAYS

摘要

A robust stabilization problem is investigated for a class of imperfectly known implicit systems with discrete and distributed time-varying delays. The delays are assumed to be unknown but bounded, with known bounds. The imperfections acting on the systems, which may be time-, state-, delayed state-, and/or input-dependent, are modelled as additive nonlinear perturbations influencing a known set of implicit nonlinear functional differential equations of the neutral type. Sufficient conditions, which include delay-dependent matrix inequalities and a delay-dependent stability criterion involving some bounding parameters for the uncertainty and delays in the system, are presented, and a class of robust feedback memoryless control inputs are designed to guarantee a prescribed asymptotic stability property for the class of implicit systems.