Delay Margin

Abstract

This chapter concerns the robust stabilization of SISO LTI systems subject to unknown delays. The fundamental issue under investigation, referred to as the delay margin problem, addresses the question: What is the largest range of delay such that there exists a feedback controller capable of stabilizing all the plants for delays within that range? Drawing upon analytic interpolation and rational approximation techniques, we develop fundamental bounds on the delay margin. Computational formulas are developed to estimate efficiently the delay margin, within which the delay plant is guaranteed to be stabilizable by a finite-dimensional LTI controller. Analytical bounds are also sought after to show explicitly how plant unstable poles and nonminimum phase zeros may fundamentally limit the range of delay over which a plant can be stabilized.