Stability analysis and H∞ control for time-delay systems

Delay-independent stability for linear time-delay systems is analyzed 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 and independent of delays, we propose a method to compute the maximum tolerable delay for which the system remains stable. Finally, the H_∞ control problem for time-delay systems is discussed and shown to be equivalent to a μ-synthesis problem. The results show that we can use the μ-approach to analyze and design for time-delay systems