基于新二重积分不等式T-S模糊系统稳定性分析

Stability Analysis for T-S Fuzzy Systems with Time Delays Via New Double Integral Inequality

针对时滞T-S模糊系统时滞相关稳定性问题,本文在文献[9]的基础上进行改进,结合模糊线积分Lyapunov泛函方法和更为先进的一重积分不等式与新型双重积分不等式,得到了保守性更低的非线性时滞系统时滞相关稳定性条件。构建合适Lyapunov-Krasovskii泛函,运用两种积分不等式技术对泛函导数进行处理,所得到的判定准则一方面能获得更大的时滞上界,降低了保守性;另外,相比完全Lyapunov泛函、时滞分割等方法减少了决策变量,为检验本文结果的有效性和优越性,通过2个数值例子进行验证。验证结果表明,比现有成果所得到的稳定性准则面能获得更大的时滞上界,减少了决策变量,而且降低了保守性和复杂度。该研究对时滞T-S模糊系统稳定性分析方法具有重要意义。

This paper is concerned with the problem of the delay-dependent stability analysis for T-S fuzzy systems with time delays.It improves the result of[9],by combining the fuzzy linear integral Lyapunov functional method with more advanced integral inequality and the new double integral inequality,animproved sufficient criterion for the delay-dependent stability analysis for T-S fuzzy systems with time delays is presented.By constructing the appropriate Lyapunov-Krasovskii functional,and the two kinds of integral inequality techniques are used to deal with the functional derivative,the obtained criterion can produce better admissible upper bounds and reduce the conservation.Compared with the complete Lyapunov functional and the delay partitioning method,it can reduce decision variables.In order to test the validity and superiority of the results in this paper,two numerical examples are used to verify the validity of the proposed method.The results show that compared with the stability criteria obtained from the existing results,our method can obtain a larger upper bound of delay,and reduce the decision variables、conservativeness and complexity.This research is of great significance for the stability analysis of time-delay T-S fuzzy systems.