The possible directions method in the theory of robust stability

This paper deals with the robust stability problem of linear uncertain systems depending on several parameters. New results are obtained by using the possible directions method for description of the boundary of the set of roots of a family of functions. This method allows one to shorten the set of extreme systems even in the case when it is a finite set or a set corresponding to the edges in the parameter space. The results may be utilized for linear systems with discrete or continuous time and any prescribed region for the roots. Also these results may be used for checking the frequency domain criteria for absolute stability of uncertain systems