Asymptotically necessary and sufficient stability conditions for discrete-time Takagi-Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials
Asymptotically necessary and sufficient stability conditions for discrete-time Takagi-Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials
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DOI：
10.1016/j.jfranklin.2013.09.025
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发表时间：
2014-02
期刊：
影响因子：
--
通讯作者：
T. Zou;Haibin Yu
中科院分区：
文献类型：
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作者：
T. Zou;Haibin Yu
讨论了具有Takagi-Sugeno形式的非线性系统的稳定性和镇定条件。采用齐次多项式非二次(HPNQ)Lyapunov函数和齐次多项式参数(HPP)状态反馈律。通过推广基于Polya定理的方法，重新给出了HPNQ Lyapunov函数和HPP控制律情形下的渐近稳定充分条件。本文的主要贡献在于给出了多指标的并行计算结果，使得松弛矩阵可以被广泛地利用来提高计算效率。数值算例验证了结果的有效性。
The stability and stabilization conditions of the nonlinear system in Takagi–Sugeno's form are considered. The homogeneously polynomially nonquadratic (HPNQ) Lyapunov functions and homogeneously polynomially parameterized (HPP) state feedback laws are adopted. By generalizing the procedure based on the Polya's theorem, the asymptotically necessary and sufficient (ANS) stability and stabilization conditions in the case of HPNQ Lyapunov functions and HPP control laws are reformulated. The major contribution of this paper is to give the parallel results using the multiple indices, so that the slack matrices can be extensively utilized to improve the numerical efficiency. The effectiveness of the results is illustrated by the numerical examples.