Transactions of the Institute of Measurement and Control vol:34 issue:4 pages:411-421
We present a numerical method to analyze the relative stability of closed-loop singleinput-single-output (SISO) dead-time systems on a given left complex half-plane for all positive delays. The well-known boundary crossing method for the imaginary axis is extended to a given vertical line stability boundary in the complex plane for these type of systems. The method allows computing the characteristic roots crossing the relative stability boundary and their corresponding delays up to a maximum predefined delay. Based on this method, we analyze the relative stability of the closed-loop system for all positive delays. Both numerical methods are effective for high-order SISO dead-time systems.