A. M. Kamachkin, G. M. Chitrov, V. N. Shamberov, “Normal matrix forms to decomposition and control problems for manydimentional systems”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2017, Volume 13, Issue 4,Pages <nobr>417

This article is cited in 4 papers

Control processes

Normal matrix forms to decomposition and control problems for manydimentional systems

A. M. Kamachkin^a, G. M. Chitrov^a, V. N. Shamberov^b

^a St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
^b St. Petersburg State Marine Technical University, Lotsmanskaya ul., 3, St. Petersburg, 190121, Russian Federation

Abstract: We wish to bring attention to the method of construction of nonsingular linear transformation in non-linear control systems. This method allows us to combine the system's dynamics' investigation of their subsystems' behavior with an admissible robust analysis. The nonsingular linear transformation matrix is the product of two matrices: one is constant and the other consists of the parameters dependent elements. The parameter's matrix reflects ambiguity of the choice of transformations and allows to increase a number of decomposition variants. Refs 29.

Keywords: many-dimensional nonlinear dynamical system, state space, state variables, nonsingular linear transformation, first natural normal form of the matrix, Jordan normal form of the matrix, decomposition of the system.

UDC: 517.977.1

Received: August 16, 2017
Accepted: October 12, 2017

DOI: 10.21638/11701/spbu10.2017.408