BROCKETT'S PROBLEM IN THE THEORY OF STABILITY OF LINEAR DIFFERENTIAL EQUATIONS

Algorithms for nonstationary linear stabilization are constructed. Com- bined with a nonstabilizabiity criterion, these algorithms result in the solution of the Brockett problem in a number of cases. x1. Introduction In the book (1), R. Brockett formulated the following problem. For a triplet of matrices A, B, and C, what conditions ensure the existence of a matrix K(t) such that the system (1) dx dt = Ax + BK(t)Cx; x 2 R n ;