Robust Luenberger-like observer for control of linear switched systems under arbitrary unknown switched function

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.