In this paper, we introduce a new sliding mode observer for Lur’e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard range of observation. Traditionally, most ofLuenberger-like observers and sliding mode observer have been designed only for uncertainties in the range of observation. Central to our approach is the treatment of the uncertainty term which we decompose into two components: the first part in the observation subspace and the second part in its complemented subspace. We establish that when the second part converges to zero, an exact sliding mode observer for the system can be obtained In scenarios where this convergence does not occur, our methodology allows for the estimation of errors between the actual state and the observer state. This leads to a practical interval estimation technique, valuable in situations where part of the uncertainty lies outside the observable range. Finally, we show that our observer is also a T-observer as well as a strong H∞ observer.

中文翻译：

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用于不确定度超出观测范围的设定值 Lur'e 系统的滑模观测器


在本文中，我们介绍了一种新的 Lur'e 集值动力学系统滑模观测器，特别是解决了不在标准观测范围内的不确定性所带来的挑战。传统上，大多数类似 Luenberger 的观测器和滑模观测器只是为观测范围内的不确定性而设计的。我们方法的核心是对不确定性项的处理，我们将它分解为两个部分：第一部分在观察子空间，第二部分在其补充子空间。我们确定，当第二部分收敛到零时，可以获得系统的精确滑模观测器在这种收敛没有发生的情况下，我们的方法允许估计实际状态和观测器状态之间的误差。这导致了一种实用的区间估计技术，在部分不确定性超出可观测范围的情况下很有价值。最后，我们证明我们的观察者也是一个 T 观察者，也是一个强 H∞ 观察者。