A Branch and Bound Methodology for Matrix Polytope Stability Problems Arising in Power Systems

C. Demarco, S. Boyd, and V. Balakrishnan

Proceedings of the IEEE Conference on Decision and Control, 6:3022-3027, December 1990.

This paper proposes a formulation to provide necessary and sufficient conditions for robust stability of a family of matrices modeling linearized power system dynamics. A construction for transforming variations in operating point into a polytope of matrices for the linearized system models is derived. Sufficient conditions to establish robust stability or instability of a polytope are developed. Finally, an iterative branch and bound technique is described that combines these tests to provide a necessary and sufficient test for robust stability of the matrix polytope.