Delay Radius of MIMO Delay Systems

Built on the development of Chap. 4, in this chapter we consider the stabilization of linear MIMO systems subject to uncertain delays. Based on tangential Nevanlinna–Pick interpolation, we develop in a similar spirit bounding sets in the delay parameter space, in which a MIMO delay plant can be stabilized by a single LTI controller. Estimates on the variation ranges of multiple delays are obtained by solving LMI problems, and further, by computing the radius of delay variations. Both the lower and upper bounds are derived. Analytical bounds show that the directions of the plant unstable poles and nonminimum phase zeros play important roles in restricting the range for stabilizability.