On delay radii and bounds of MIMO systems

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 (SISO) systems with a linear time-invariant (LTI) controller, this margin is known to be finite for an unstable plant, and bounds on the delay margin are available. This paper extends the existing results to multi-input multi-output (MIMO) 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 constraint is imposed by the pole on that delay, while if the delay direction is parallel to that of a nonminimum phase zero, its allowable range will be further restricted by the nonminimum phase zero.