Robust stabilization of linear systems with time-varying point delays via a delay-free dynamic controller

^** Email: wepdepam{at}lg.ehu.es This paper deals with the problem of robust closed-loop stabilizationagainst parametrical uncertainties of linear systems subjectto internal (i.e. in the state) and external (i.e. in the output),possibly time-varying and unbounded point delays of a boundedtime-derivative. The output-feedback linear stabilizing controlleris delay free and dynamic. It is assumed that the undelayedplant (i.e. the delay-free part of the plant) is stabilizableand detectable. The synthesis process of the stabilizing controllerinvolves three major actions. First, an augmented system isbuilt with the dynamic equations of both plant and controller.At this step, the controller structure is available but a particularstabilizing controller parametrization still remains undetermined.Subsequently, a Lyapunov matrix equation is ensured to be solvablefor the augmented closed-loop delay-free system so that sucha system is stable with a large stability abscissa related tothe amounts of uncertainties and delay contributions to thedynamics. At this stage, one takes the advantage that the augmentedsystem may be stabilized by an appropriate dynamic controllerof minimum order since the undelayed plant is stabilizable anddetectable. Finally, a complementary matrix equality is manipulatedto establish the closed-loop stability tolerance of the augmenteddelay system, related to that of the delay-free one, to thedelayed dynamics and parametrical uncertainties.