We study the problem of observer design for feedback control purposes of switched linear systems in which the switching function is entirely unknown. We propose a Luenberger-like observer to implement feedback control. By a state transformation, the original system is immersed into another one that has constant parameters, but is affected by unknown inputs and jumps in the state. The main advantages of the obtained observer are that neither a dwell-time is required nor any differentiation is needed. Thus, this methodology may be useful for the case of any arbitrary switching function; that is, the knowledge of a dwell-time is not required. If, however, an average dwell-time is known, then the proposed observer may still be implemented. Further, we show that the overall system is robust with respect to parametric uncertainties. The consequence of this robustness is that the whole system keeps its stability property when the matrices of the system take values in a set larger than the one considered by the indexed set. We carry out simulations to illustrate the effectiveness of the proposed methodology.

中文翻译：

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在任意未知切换函数下控制线性切换系统的鲁棒类 Luenberger 观测器

我们研究了用于反馈控制目的的观察器设计问题，其中开关函数是完全未知的。我们提出了一个类似 Luenberger 的观察者来实现反馈控制。通过状态转换，原始系统陷入另一个具有恒定参数但受未知输入和状态跳跃影响的系统中。获得的观测器的主要优点是既不需要停留时间也不需要任何区分。因此，这种方法对于任何任意切换函数的情况都可能有用；也就是说，不需要了解停留时间。然而，如果平均停留时间是已知的，则仍然可以实施建议的观察器。此外，我们表明整个系统在参数不确定性方面是稳健的。这种鲁棒性的结果是，当系统的矩阵取值大于索引集所考虑的值时，整个系统保持其稳定性。我们进行了模拟以说明所提出方法的有效性。