Thirty Two Edge Theorem for the Robust Stability of Time Delay and Distributed Parameter Systems with an Interval Uncertainity Model

This paper extends recent results on the parametric approach to robust stability of time delay and distributed parameter systems. A new edge type result is given for uncertain systems described by a family of characteristic quasipolynomials being a particular polytope: a sum of N interval polynomials each multiplied by an analytic function in the right halfplane. The result is: To chek the robust stability it is sufficient to check the stability of only 4^NN predetermined edges of the multidimensional polytope. In an important particular case of an interval rational plant with input delay this means checking 32 distinguished edges.