多項式カーネルを用いた非線形システムの安定性の数値的解析方法*

摘要

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.