Observability and Detectability of Singular Linear Systems with Unknown Inputs

International audienceIn this paper the strong observability and strong detectability of a general class ofsingular linear systems with unknown inputs are tackled. The case when the matrix pencil is non-regular is comprised (i.e., more than one solution for thedifferential equation is allowed). It is shown that, under suitableassumptions, the original problem can be studied by means of a regular(non-singular) linear system with unknown inputs and algebraic constraints.Thus, it is shown that for purposes of analysis, the algebraic equations canbe included as part of an extended system output. Based on this analysis, weobtain necessary and sufficient conditions guaranteeing the observability (or detectability) of the system in terms of the zeros of the system matrix.Corresponding algebraic conditions are given in order to test theobservability and detectability. A formula is provided that expresses thestate as high order derivative of a function of the output, which allows forthe reconstruction of the actual state vector. It is shown that the unknown inputs may be reconstructed also