Search method for the matrix multiplier time constant and the weighting matrix of the multivariable Popov stability criterion

Abstract

The multivariable Popov stability criterion contains two arbitrary diagonal matrices which are called the weighting matrix and the multiplier time constant matrix. The choice of the matrices determines the sharpness of the stability criterion obtained. In this paper, a method of searching for adequate values of the matrices is proposed. The method is based on the relation between the M-matrix and the positive-definite hermilian matrix. Numerical examples show that this method is useful in obtaining a sharper stability condition.