Abstract
It is known that the controllable system x′ = Bx + Du, where the x is the n-dimensional vector, can be transferred from an arbitrary initial state x(0) = x 0 to an arbitrary finite state x(T) = x T by the control function u(t) in the form of the polynomial in degrees t. In this work, the minimum degree of the polynomial is revised: it is equal to 2p + 1, where the number (p − 1) is a minimum number of matrices in the controllability matrix (Kalman criterion), whose rank is equal to n. A simpler and a more natural algorithm is obtained, which first brings to the discovery of coefficients of a certain polynomial from the system of algebraic equations with the Wronskian and then, with the aid of differentiation, to the construction of functions of state and control.
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This work was supported by the Russian Foundation for Basic Research, project no. 07-01-00397.
Original Russian Text © S.P. Zubov, E.V. Raetskaya, Le Hai Trung, 2008, published in Avtomatika i Telemekhanika, 2008, No. 11, pp. 41–47.
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Zubov, S.P., Raetskaya, E.V. & Trung, L.H. On polynomial solutions of the linear stationary control system. Autom Remote Control 69, 1852–1858 (2008). https://doi.org/10.1134/S0005117908110027
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DOI: https://doi.org/10.1134/S0005117908110027