Robust stabilizability of MIMO delay systems: Bounds on delay radii

The delay margin of a time-delay system constitutes the fundamental limit beyond which no single controller may exist to robustly stabilize an unstable delay plant for a range of delay values. For single-input single-output systems with a linear time-invariant controller, this margin is known to be finite, and bounds on the delay margin are available. This paper extends the existing results to multi-input multi-output systems. We derive upper bounds on a generalized notion called delay radius. Our results show that for a delay whose direction is orthogonal to that of an unstable pole, no limit is imposed by the pole, while if the delay direction is parallel to that of a nonminimum phase zero, its allowable range is further restricted.