Method of robust stability analysis with highly structured uncertainties

Abstract

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi = \det [I + FH]</tex> 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.