Abstract
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.
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This research is supported partly by the National Natural Science Foundation of China under Grant Nos. 60674022, 60736022, and 60221301.
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Li, Z., Qiao, Y., Qi, H. et al. STABILITY OF SWITCHED POLYNOMIAL SYSTEMS. J Syst Sci Complex 21, 362–377 (2008). https://doi.org/10.1007/s11424-008-9119-5
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DOI: https://doi.org/10.1007/s11424-008-9119-5