For non-linear positive switched systems (NPSSs) with time-varying delay, the $H_{\infty }$ estimation problem is addressed in this paper. Firstly, in light of T-S fuzzy modeling method, the considered NPSS is equivalently transformed into a switched positive T-S fuzzy system. Then, a less conservative $H_{\infty }$ performance co1ndition is provided for the error system via presenting a new piecewise quadratic copositive Lyapunov–Krasovskii functional. Furthermore, an observer is constructed to make the underlying system exponentially stable with a preset $H_{\infty }$ performance and an iterative optimization algorithm is proposed to obtain the observer parameters. To verify the effectiveness of the theoretical results, two examples are finally presented.

中文翻译：

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具有时变延迟的非线性正切换系统的 H∞ 估计

对于具有时变延迟的非线性正切换系统（NPSS），本文解决了$H_{\infty}$估计问题。首先，根据TS模糊建模方法，将考虑的NPSS等价转化为切换正TS模糊系统。然后，通过提出一个新的分段二次共正 Lyapunov-Krasovskii 泛函，为误差系统提供了一个不太保守的 $H_{\infty }$ 性能条件。此外，构造了一个观察器，使底层系统以预设的$H_{\infty}$性能指数稳定，并提出了一种迭代优化算法来获得观察器参数。为了验证理论结果的有效性，最后给出了两个例子。