Observability recovering by additional sensor implementation in linear structured systems

In this paper, we consider linear structured systems which represent a large class of parameter dependent linear systems. We focus our attention on observability analysis. It turns out that the system is structurally observable if and only if the system is output connected and contains no contraction. We analyze in a structural way the possible causes for unobservability and tackle the problem of observability recovering by additional sensor implementation. Using classical tools of graph theory, we give the minimal number and the location of additional sensors to be implemented in order to avoid contractions. We give also the minimal number of states which have to be measured for ensuring output connectivity. We think that the results presented here provide a deeper understanding of structural unobservability and can be useful for solving problems as fault detection without a priori assuming the system observability.