In this article, the design problem of ℓ₂–ℓ_∞ proportional–integral observer (PIO) is investigated for a class of discrete‐time systems with mixed time‐delays. The mixed time‐delays comprise both the discrete time‐varying delays and infinitely distributed delays. The round–robin protocol (RRP) is employed to schedule the data transmissions from the sensors to the observer so as to mitigate the communication burden and prevent the data collisions. A novel PIO is developed whose observer gain is dependent on the data transmission order as a reflection of the effects induced by the RRP scheduling. By resorting to the token‐dependent Lyapunov functional and the matrix inequality technique, the desired PIO is designed with exponentially stable error dynamics of the state estimation and guaranteed ℓ₂–ℓ_∞ disturbance attenuation/resistance capacity. Finally, a simulation example is exploited to verify the validity of the proposed observer design method.

中文翻译：

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轮询协议下混合时滞系统的ℓ2-ℓ∞比例积分观测器设计

在这篇文章中，设计问题ℓ ₂ - ℓ _∞研究了一类具有混合时滞的离散时间系统的比例积分观测器（PIO）。混合时延既包括离散时变延迟，又包括无限分布的延迟。轮循协议（RRP）用于安排从传感器到观察者的数据传输，从而减轻通信负担并防止数据冲突。开发了一种新颖的PIO，其观察者增益取决于数据传输顺序，以反映RRP调度引起的影响。通过诉诸令牌相关Lyapunov函数和矩阵不等式技术，期望的PIO被设计为状态估计的指数稳定的误差动力和保证ℓ ₂ - ℓ _∞干扰衰减/抵抗能力。最后，通过仿真实例验证了所提出的观测器设计方法的有效性。