STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of (switched) polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a (switched) polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some su±cient conditions for the global stability of polynomial systems. This research is supported partly by the National Natural Science Foundation of China under Grant Nos. 60674022, 60736022, and 60221301.