Numerical Approach to Robust Stability Test of Mixed Uncertain Systems

The robust stability analysis of mixed uncertain systems　can be completed by testing the H_∞ norm of edges of an uncertain　rational function. To reduce the computational complexity, a numerical　approach is proposed for a class of mixed uncertain systems whose　coefficients affinely dependent on system parameters. It is shown　that the image of an edge rational function at a fixed frequency is an arc in s-plane. Further, a new formula to compute the maximal norm of the　arc is developed. Based on these results an edge test algorithm in a finite　frequency range is induced by which the computational burden can be greatly　reduced.