New stability criterion for positive impulsive fuzzy systems by applying polynomial impulse-time-dependent method

Likui Wang, Bo Zheng, Hak-Keung Lam

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Abstract

The problems of exponential stability and <inline-formula> <tex-math notation="LaTeX">$L_{1}$</tex-math> </inline-formula>-gain for positive impulsive Takagi&#x2013;Sugeno (T&#x2013;S) fuzzy systems are further studied in this article. Different from the Lyapunov function in the literature, where the Lyapunov matrices are time-invariant or only linearly dependent on the impulse interval, in this article, a novel polynomial impulse-dependent (ID) copositive Lyapunov function (CLF) is constructed by using the polynomial impulse time function. In addition, the binomial coefficients are applied to derive new finite linear programming conditions. Less conservative results are obtained since the polynomial ID CLF contains more impulse interval information. Three examples demonstrate the influence of the polynomial degree on the results and the effectiveness of the developed new results.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalIEEE Transactions on Cybernetics
DOIs
Publication statusPublished - 10 Feb 2024

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