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

Likui Wang; Bo Zheng; Hak-Keung Lam

doi:10.1109/TCYB.2024.3370102

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 L1-gain for positive impulsive Takagi-Sugeno (T-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 language	English
Pages (from-to)	5473-5482
Number of pages	10
Journal	IEEE Transactions on Cybernetics
Volume	54
Issue number	9
DOIs	https://doi.org/10.1109/TCYB.2024.3370102
Publication status	Published - 10 Feb 2024

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New Stability Criterion for_WANG_Accepted_GREEN AAMAccepted author manuscript, 1.06 MB

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

abstract = "The problems of exponential stability and L1-gain for positive impulsive Takagi-Sugeno (T-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.",

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AU - Zheng, Bo

AU - Lam, Hak-Keung

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Y1 - 2024/2/10

N2 - The problems of exponential stability and L1-gain for positive impulsive Takagi-Sugeno (T-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.

AB - The problems of exponential stability and L1-gain for positive impulsive Takagi-Sugeno (T-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.

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JO - IEEE Transactions on Cybernetics

JF - IEEE Transactions on Cybernetics

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

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