Structured and Simultaneous Lyapunov Functions for System Stability Problems
S. Boyd and Q. Yang
International Journal of Control, 49(6):2215-2240, 1989.
It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of dx/dt=Ax for some appropriate A. The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple numerical example is given.