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Method of robust stability analysis with highly structured uncertainties

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1 Author(s)
Saeki, M. ; University of Tsukuba, Sakura-mura, Niihari-gun, Ibaraki, Japan

This paper presents a method of analyzing the stability of linear time-invariant interconnected systems with uncertainties: each subsystem is single-input single-output and its vector locus lies inside a polygon at each frequency. It is shown that the convex closure of the image of the Cartesian product of these polygons under the mapping \phi = \det [I + FH] agrees with the convex closure of the image of the vertices of these polygons under the mapping φ. From this result the image can be estimated by a finite Dumber of calculations. A sufficient stability condition is obtained by applying this result to the multivariable Nyquist stability criterion.

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Automatic Control, IEEE Transactions on  (Volume:31 ,  Issue: 10 )