The thrust of the project is to develop an algorithm to partition an unstable standard polytope of polynomials into stable and unstable regions. This will be an extension of the Principal Investigator's work for the partition of unstable polygons of polynomials (convex hull of finitely many coplanar polynomials). Since the strong theoretical foundation for the resolution of this problem has already been laid in the Principal Investigator's earlier work, a reasonable solution of the partition problem for polytopes looks quite promising. It is also proposed that the partition approach has several useful practical applications. For example, this approach could be utilized to find a controller that would stabilize a given uncertain plant with affine coefficients in the parameters over a certain compact domain of its uncertainty. The concept of Youla's parameterization of all stabilizing controllers for a nominal plant is utilized to achieve this end. Another potential application is to obtain maximal robustness bounds for the parameters involved in the characteristic polynomial of a control system when the coefficients are affinely dependent on the parameter vector. A possible approach for this is to partition the unstable polytope generated by the characteristic polynomials and identify the maximal domain of parameter vector by identifying the values of the parameter vector corresponding to the boundary of the partition.
