Description of the Structure of Irregularity Sets of Linear Differential Systems with a Linear Parameter

We consider the class of linear parametric differential systems defined on the half-line , where is a parameter, , and the matrix is piecewise continuous and bounded. It is proved that for each some set is the irregularity set of one of such systems (i.e., the set of for which this system is Lyapunov irregular) if and only if it is a -set of the real line not containing zero. The necessity of the above conditions has been established earlier. This assertion solves the problem posed by N.A. Izobov in the early 1990s.