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R.A. Horn, C.R. Johnson (1985)
Matrix Analysis
Differential Equations, Vol. 39, No. 12, 2003, pp. 1713–1723. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 12, 2003, pp. 1627–1636. Original Russian Text Copyright c 2003 by Popova. ORDINARY DIFFERENTIAL EQUATIONS Global Controllability of the Complete Set of Lyapunov Invariants of Periodic Systems S. N. Popova Institute for Mathematics and Computer Science, Udmurt State University, Izhevsk, Russia Received December 2, 2002 Consider the linear control system n m x _ = A(t)x + B(t)u; x 2 R;u 2 R;t 2 R; (1) with bounded piecewise continuous matrix coecients A()and B()on R. Suppose that the control u() in system (1) is de ned by the feedback principle u = Ux,where the m n matrix U ()is also assumed to be bounded and piecewise continuous. Then system (1) becomes the closed system x _ =(A(t)+ B(t)U )x; x 2 R;t 2 R; (2) with bounded piecewise continuous coecients, for which invariants of Lyapunov transformations [1, p. 245; 2, p. 42] are de ned. We arrive at the problem as to whether it is possible to construct a control U () such that some Lyapunov invariant (for example, the complete spectrum of Lyapunov exponents [3, p. 145]) of system (2) with this
Differential Equations – Springer Journals
Published: Oct 5, 2004
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