H disturbance attenuation for state delayed systems

In this note, the differential game and dissipation inequality are applied to the disturbance attenuation or H^∞-control for linear systems with delayed state. Firstly, a simple sufficient condition on the existence of a γ-suboptimal H^∞ state feedback controller is given, which is independent of delay, and an observer-based dynamic output feedback solution is presented in terms of Riccati inequalities (or Riccati equations). Secondly, a sufficient condition on the existence of a delay-dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods.