Two-level stabilization of a multiply connected system with a periodic matrix of coefficients by piecewise constant control

The paper considers a multiply connected controllable dynamical system with a periodic matrix of coefficients and piecewise constant control. Conditions are found for two-level stabilization of the equilibrium position of the specified system when local controls stabilize the equilibrium position of individual linear subsystems, and global control acts on intersystem connections. For this, a transition is made from the original system with periodic matrices to an auxiliary system with piecewise constant matrices of coefficients, for which an estimate of the approximate monodromy matrix is found.