Numerical Analysis of Stability of Nonlinear Dynamical Systems using Polynomial Kernel Functions

Abstract

We describe a tractable numerical procedure using polynomial kernel functions to prove the nonexistence of Lyapunov functions. The algorithm terminates in polynomial time of the dimension of the state space, the number of sample states, the degree of the polynomials appear in the system,and the degree of the Lyapunov candidate polynomial functions. The algorithm is also avairable to construct Lyapunov functions with SOS techniques. We demonstrate the appearance by some simple numerical examples.