A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the true state and inputs. The proposed observer can be designed using semidefinite programming with LMI constraints and is optimal in the minimum \mathcal{H}_{\infty}-norm sense. We show that the strong detectability of each constituent linear time-invariant system is a necessary condition for the existence of such an observer, as well as the boundedness of set-valued estimates. Furthermore, sufficient conditions are provided for the upper bounds of the estimation errors to converge to steady state values and finally, the results of such a set-valued observer are exhibited through an illustrative example.

中文翻译：

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线性参数变化系统的同时输入和状态集值\mathcal{H}_{\infty}-观察者

针对具有有界范数噪声和完全未知攻击信号的线性参数变化系统，提出了一种固定阶集合值观测器，该系统同时找到有界状态集和包括真实状态和输入在内的未知输入。所提出的观测器可以使用具有 LMI 约束的半定规划来设计，并且在最小 \mathcal{H}_{\infty} 范数意义上是最优的。我们表明，每个组成线性时不变系统的强可检测性是存在这样一个观察者的必要条件，也是集值估计的有界性。此外，为估计误差的上限收敛到稳态值提供了充分条件，最后，通过说明性示例展示了这种设置值观测器的结果。