Stability analysis and H∞ control for time-delay systems

Delay-independent stability for linear time-delay systems is analyzed in this paper using the structured singular value concept. We show that the delays can be viewed as repeated scalar uncertainty blocks for a 'nominal' plant, and the stability analysis converts to checking the structured singular value of the nominal plant with respect to a specially constructed uncertainty structure. When the system is not stable independent of delays, we propose a method to compute the maximum tolerable delay for which the system remains stable. Finally, H-infinity control problem for time-delay systems is discussed and shown to be equivalent to a mu-synthesis problem. The results show that we can use mu-approach to analyse and design for time-delay systems.