Abstract
Using the semi-tensor product method, this paper investigates how to represent the polynomial nonlinear system as the matrix and studies the stability of a class of the polynomial nonlinear systems. First, we represent polynomial nonlinear systems as the matrices via semi-tensor product method. Second, we construct and calculate Lyapunov function by using the semi-tensor product method. Third, we get a theorem of judging whether a class of polynomial nonlinear systems are asymptotically stable through semi-tensor product method. Finally, the study of an illustrative example shows that the new theorem of judging the stability of nonlinear systems in this paper is very effective.
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