A new, convexity based, necessary and sufficient vertex solution for robust stability check of linear interval parameter matrix families

This paper revisits the problem of checking the robust stability of matrix families generated by interval parameters in a matrix. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices, making the `convexity´ property non-transparent. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more `elegant´ than the previous solution. In other words, the new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm.