Random search of stable member in a matrix polytope (Q738955)

The authors propose a random searching algorithm of a stable member for special classes of matrix families. Specifically, (i) the stability region is determined for a one-parameter nonlinear \(n\times n\) family. For a multi-parameter family, a nonlinear version of the random search D-decomposition method is proposed. (ii) The stability region is determined for the \(3\times 3\) interval family with constant diagonals. In the case of non-constant diagonals, random search of a stable member is proposed. (iii) A necessary and sufficient condition for the existence of a stable member is obtained for the \(n\times n\) interval family with nonnegative off-diagonal intervals.