Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System

We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori basis of the configuration space) in the transformation groups GL n (ℝ) and SO n minimizing the mismatch between the positional force matrix and its reference rated parameters. Based on Morse theory, we construct a nonlinear matrix characteristic equation of the optimal SO n -adjustment process. The results have applications in the differential precise modeling of forced oscillations and generate statements of the problem in the infinite-dimensional case.