We are considering the problem of sampled-data observer design for nonlinear time-varying systems that are state-affine. The novelty lies in that both distributed and discrete delays are considered in the output equation. The latter is also subject to a parameter uncertainty of nonaffine nature due to output sampling. Interestingly, all system delays are modeled using a single distributed representation, involving a distribution function, allowing thus for a unified treatment of delays. A Kalman-like observer is developed to cope with both state and parameter uncertainty. Its main components are (i) a time-varying-gain state-estimator involving both output and parameter rate injections; (ii) a distributed-nature adaptive output-predictor that compensate for all delay effects, including that of output sampling; (iii) an parameter-estimator that is optimized in the sense that it makes use of all available information. The resulting observer is shown to be exponentially convergent, for small delays and sampling intervals, provided the input signal is sufficiently exciting. The analysis is performed using a Lyapunov–Krasovskii functional, Halanay's lemma, Wirtinger's inequality, and other tools.

中文翻译：

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具有分布式和离散输出延迟的状态和参数仿射系统的采样数据自适应观测器

我们正在考虑状态仿射的非线性时变系统的采样数据观测器设计问题。新颖之处在于在输出方程中同时考虑了分布式延迟和离散延迟。由于输出采样，后者还受到非仿射性质的参数不确定性的影响。有趣的是，所有系统延迟都使用单个分布式表示进行建模，涉及分布函数，从而允许对延迟进行统一处理。开发了类卡尔曼观测器来处理状态和参数的不确定性。它的主要组成部分是 (i) 一个时变增益状态估计器，包括输出和参数速率注入；(ii) 一种分布式自适应输出预测器，可补偿所有延迟效应，包括输出采样的延迟效应；(iii) 一个参数估计器，在它利用所有可用信息的意义上进行了优化。如果输入信号足够令人兴奋，那么对于小的延迟和采样间隔，结果观察器显示为指数收敛。使用 Lyapunov-Krasovskii 泛函、Halanay 引理、Wirtinger 不等式和其他工具进行分析。