Time-optimal control and the trigonometric moment problem

An analytic solution of a time-optimal problem for the oscillatory system
$$ \dot{x}=Ax+bu,\qquad|u|\leqslant1,\quad\operatorname{rank}(b,Ab,\dots,A^{n-1}b)=n, $$
is given, where the spectrum $\sigma(A)=\{\pm ik\lambda,k=0,1,\dots,p;\lambda>0\}$. Introducing a special system of trigonometric polynomials (canonical variables) and studying Toeplitz determinants in these variables, the authors obtain equations for determining the control time, as well as the points and surfaces of switching the optimal control. The solution thus obtained is, on the other hand, the solution of a trigonometric moment problem on the smallest possible interval in the form of a function of a $(-1,1)$-moment sequence. The question of local equivalence of linear time-optimal problems is considered for systems with a one-dimensional control.
Bibliography: 6 titles.