Analytical Identification of Polynomial Nonlinear Systems With Uncontrollable Linearization

Recently, system identification (SID)based on center manifold (CM) is proposed to identify polynomial nonlinear systems (PNSs) analytically. With this method, estimating the unknown parameters in the PNSs is converted to the problem of solving a set of recursively defined Sylvester equations (RSEs). However, existing CM-based SID algorithm assumes the linearization of the PNS to be controllable. In this note, we propose a more general framework which allows for uncontrollable linearizations. By a new formulation of the RSEs, it is shown that controllability can be attained in the high-order RSEs, so that the frequency-domain subspace SID method can be invoked to identify all the parameters in the PNS. Consistency is proved if a set of persistence of excitation conditions is satisfied.