H∞ optimal control of linear time-varying systems with time-varying delay via a controllability approach

This paper addresses the H-infinity optimal control problem for a class of uncertain linear time-varying delay systems. The interesting features here arc that the system in consideration is non-autonomous, the state delay is time-varying, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. Based on the Lyapunov-Krasovskii Functional method, we show that the H-infinity optimal control problem for the system has a solution if some appropriate linear control delay-like system is globally controllable.