H-infinity and positive-real control for linear neutral delay systems

This note is concerned with the H-infinity and positive-real control proble ms for linear neutral delay systems. The purpose of H-infinity control is t he design of a memoryless state feedback controller which stabilizes the ne utral delay system and reduces the H-infinity norm of the closed-loop trans fer function from the disturbance to the controlled output to a prescribed level, while the purpose of positive-real control is to design a memoryless state feedback controller such that the resulting closed-loop system is st able and the closed-loop transfer function is extended strictly positive re al. Sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality (LMI). When this LMI is feasib le, the expected memoryless state feedback controllers can be easily constr ucted via convex optimization.