Stability verification for energy-aware hydraulic pressure control via simplicial subdivision

This paper presents a linear programming-based method for finding Lyapunov functions of dynamical systems with polynomial vector fields. We propose to utilize a certificate of positivity in the Bernstein basis based on subdivisioning to find a Lyapunov function. The subdivision-based method is proposed since it has better degree bounds than similar methods based on degree elevation. The proposed method is successfully applied to find a Lyapunov function for a pressure controlled water distribution system.