Achievable delay margin using LTI control for plants with unstable complex poles

Abstract

We consider the achievable delay margin of a real rational and strictly proper plant, with unstable complex poles, by a linear time-invariant (LTI) controller. The delay margin is defined as the largest time delay such that, for any delay less than this value, the closed-loop stability is maintained. Drawing upon a frequency domain method, particularly a bilinear transform technique, we provide an upper bound of the delay margin, which requires computing the maximum of a one-variable function. Finally, the effectiveness of the theoretical results is demonstrated through a numerical example.Keywords delay margin, systems with time-delay, time-invariant systems, unstable complex poles, frequency domain method CitationJu P J, Zhang H S. Achievable delay margin using LTI control for plants with unstable complex poles. Sci China Inf Sci, 2018, 61(9): 092203, https://doi.

An Analytic Interpolation Approach to Stability Margins With Emphasis on Time Delay

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“…The nominal complementary sensitivity function T 0 was introduced as a the center of the ball to which the analytic interpolantT is confined, as shown in (21) and (22). However, T 0 also has a systems theoretic interpretation.…”

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