State space method in the identifiability problem of linear nonstationary singularly perturbed systems

The identifiability problem is studied for linear nonstationary singularly perturbed systems of differential equations by the state space method. We consider the case where the linear combinations of coefficients of an unknown slowly-varied function additively enter the right-hand side of a linear nonstationary singularly perturbed system, a solution to a differential equation with an unknown initial condition. Effective tests that are necessary and sufficient conditions of a rank type for the identifiability of this linear nonstationary singularly perturbed system are obtained in terms of solutions to its algebraic defining equations. An example that illustrates an application of the obtained results is presented.