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A note on two methods related to stability robustness of polynomials in a sector (relative stability)

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2 Author(s)
Katbab, A. ; Dept. of Electr. Eng. & Comput. Sci., George Washington Univ., Washington, DC, USA ; Jury, E.I.

Two recent results on the stability robustness of uncertain systems (polynomials) are addressed. One gives a vertex test for left-sector (relative) stability, where the number of the required vertices is four for a real case and eight for a complex case. The other gives an elegant frequency-domain graphical (hodograph) approach for left-plane stability, where the plotting of only one (two for a complex case) hodograph plus simple boundary conditions is both necessary and sufficient to obtain the maximum coefficient perturbation bounds. It is shown that a similar graphical test exists for the left-sector stability case

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Automatic Control, IEEE Transactions on  (Volume:38 ,  Issue: 2 )