In this paper, the issues about weighted \(H_\infty\) performance analysis and \(H_\infty\) control for the stochastic switched nonlinear systems (SSNSs) with multiplicative noise are investigated. The mode-dependent average dwell time (MDADT) method is used to deal with the switching in different modes. Firstly, we get a sufficient condition to show that the considered system with all stable subsystems achieves the exponential stability in mean square sense and a specified weighted \(H_\infty\) performance, which is extended to the case that both stable and unstable subsystems coexist in terms of second-order Hamilton-Jacobi inequalities (HJIs). Then, by using Takagi-Sugeno (T-S) fuzzy approach, the \(H_\infty\) controller for SSNSs is designed via solving a set of linear matrix inequalities (LMIs). Finally, an example is supplied to illustrate the effectiveness of our results.

中文翻译：

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非线性随机切换系统的加权$$ \ mathbf {H} _ \ infty $$ H∞性能分析：一种与模式有关的平均停留时间方法

本文研究了具有乘法噪声的随机切换非线性系统（SSNS）的加权\（H_ \ infty \）性能分析和\（H_ \ infty \）控制问题。依赖于模式的平均停留时间（MDADT）方法用于处理不同模式下的切换。首先，我们有充分的条件表明所考虑的具有所有稳定子系统的系统在均方意义上具有指数稳定性，并具有指定的加权\（H_ \ infty \）性能，这扩展到了稳定子系统和不稳定子系统的情况在二阶汉密尔顿-雅各比不等式（HJI）方面共存。然后，通过使用Takagi-Sugeno（TS）模糊方法，\（H_ \ infty \）通过解决一组线性矩阵不等式（LMI）设计用于SSNS的控制器。最后，提供一个示例来说明我们的结果的有效性。