Finite Verification of the Characteristic Specification of Discrete Systems

Positive real functions are of significance in absolute stability and passivity analysis.The characteristic specification δ[·] of systems is closely related to positive real functions.For a family of systems with uncertain parameters, the determination of the minimal value of their characteristic specifications is the main focal point of the present note. We denote the nth, mth order real polynomial sets (n>m) by F={f(z)|f(z)=az~n+az+…+az+a, a≠0}, G={g(z)|g(z)=bz~m+bz+…+bz+b, b≠0}.