Stability and the eigenvalues ofG(s)

Abstract

A multivariable feedback system y¯(s) = G(s)x(s). x¯(s)=ū(s) − F(s)y(s) is considered, where G(s δ (gkl(s) is the n × n plant transfer matrix and f(s) = diag (f 1) [tdot] f 2(s) [tdot] f n(s)). By imposing some restrictions on the structure of G(s), we may use the eigenvalues λj(s), 1≤j≤n of G(s) to infer the stability of the closed-loop system in an arbitrary rectangular region Φ δ{F − ∞αk≤ƒkβk≤∞, 1≤k≤n}, which is a set of positive Lebesgue measure. The stability result contains Rosenbrock's stability theorem as a special case.