Observability recovering for linear switched systems via sensor placement: a graphic approach

It is well known that the state observability of switched linear systems depends strongly on the switching sequence between the modes. In this work, the problem of recovering the observability of a class of switched linear systems via sensor placement is treated. The proposed method is based on an original graph representing switched systems and allowing to handle the problem of the sensor placement. Such graph-theoretic approach, needs only the knowledge of the system's structure. The calculations in order to find the number and location of the necessary sensors are given in terms of paths on a digraph and matchings on a bipartite graph which are particularly intuitive. Moreover, these results can be implemented with classic algorithms of the graph theory.