Inverse LQ approach to robust stabilization of linear systems with input delay

The Inverse LQ design is extended to linear input-delayed systems and is modified so as to ensure robust stability of the resulting LQ regulator against a given uncertainty of delay time. This extension is done by reducing the ILQ design for an original delayed system to that for another related system without delay, based on the LQ design theory for input-delayed systems. Modification of the ILQ regulator described above is done by reducing a robust stabilization problem based on the small gain theorem into a quadratic stabilization problem for an augmented system with the frequency weight associated with the delay uncertainty. Applying a known result regarding to this problem, namely the robust ILQ design method, yields a desired design procedure for robust stabilization.