LYAPUNOV FUNCTION COMPUTATION FOR AUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS USING SUM-OF-SQUARES PROGRAMMING

摘要

We study the global asymptotic stability in probability of the zero solution of linear stochastic differential equations with constant coefficients. We develop a sum-of-squares program that verifies whether a parameterized candidate Lyapunov function is in fact a global Lyapunov function for such a system. Our class of candidate Lyapunov functions are naturally adapted to the problem. We consider functions of the form V(x) = ||x||(P)(Q) := (x(inverted perpendicular) Qx)(P/2), where the parameters are the positive definite matrix Q and the number p > 0. We give several examples of our proposed method and show how it improves previous results.