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In this note, we present an effective solution to the stabilization of linearinput delay systems subject to dissipative constraints while all the effect ofinput delay is compensated by a controller with novel structure. The method isinspired by the recent development in the mathematical treatment of distributeddelays and predictor controllers, which are critical for the derivation of thesolution. An important conceptual innovation is the use of a parameterizeddynamical state feedback controller (DSFC), where the dimension of thecontroller equals the dimension of the control input. A sufficient conditionfor the existence of a dissipative DSFC is obtained via the Krasovskiifunctional approach, where the condition includes a bilinear matrix inequality(BMI). To solve the BMI, we apply an inner convex approximation algorithm whichcan be initialized based on an explicit construction of a predictor controllergain. The proposed DSFC can be considered as an extension of the classicalpredictor controller, thereby capable of compensating all the effects of thepointwise input delay while satisfying dissipative constraints. A numericalexample is given to illustrate the effectiveness of our proposed methodology.

Dissipative stabilization of linear input delay systems via dynamical state feedback controllers: an optimization based approach