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Abstract
In this paper, it has been shown that a high-order system can be reduced to a low-order-system based on Sturm's sequence. If the original system is stable, the low-order system is also stable. The time responses of the low-order model closely approximates the original system response.
It is also shown that the relative stability parameters namely the gain-margin and the phase-margin can also be obtained from the low-order system, which compare favourably with those of the original system. This has been illustrated with numerical examples. The analytical method explained here is simple and straight forward, when compared to the tedious graphical methods in finding the relative stability of a high-order system. The results obtained by this purely analytical method are closer to the computed values of the original system than those obtained by existing methods.