Contesting Conservatism with Complexity: Exploring Linear Relaxations of the Positivstellensatz for Robust Stability Analysis of Nonlinear Systems

Lyapunov's 2nd method can be formulated as a convex optimization problem by means of Sum-of-Squares (SOS) optimization. This gives a powerful tool for robust stability analysis of nonlinear systems. The use of SOS optimization is limited to small dynamical systems, because of the demanding numerical complexity underlying SOS optimization. For...