Rank and order conditions for identifiability analysis of linear systems with standard parameterized control and observation matrices

In present paper the approach to testing generically both local and global identifiability of linear large scale systems based on rank and order conditions is further developed. This method was initially proposed for the most general case of parametrization when estimated parameters are the elements of system matrices with linear constraints on them. Here we adapt the approach for the more special case when we have standard form of control and observation matrices with only one nonzero element, which can be estimated, in each row (column) of observation (control) matrix. Despite this limitation such model structures are often used in practice, for example, in compartmental modeling. Taking into account special structure of this class of model structures we succeed in decreasing the dimensions of the identifiability matrices in the rank conditions that is significant for the symbolic computations of generic rank. Along this way we have obtained the so called order conditions - relations between the number of constraints and the dimensions of system matrices - that could be useful at the first stages of modeling allowing discard the whole bunch of non-identifiable model structures. An example is given to illustrate the approach.