Constructing Lyapunov Functions for Nonlinear Delay-Differential Equations using Semidefinite Programming

The search for a polynomial Lyapunov function proving delay-independent stability of multivariate nonlinear polynomial delay differential equations is approached using semidefinite programming. The functional non-negativity constraints are tightened to be sum of squares constraints, a condition which is computationally feasible to check. The algorithm uses recent advances in computational semi-algebraic geometry.