Аннотация:Conditions about the problem of robust stability for systems of differential equations with bounded external perturbations are obtained from the solution of the problem of maximum deviation using an extension of definition of Duboshin and Malkin on stability under permanent perturbations. Further a linear controlled system with close-loop control is under consideration. Solutions of minimax stabilization problem and a problem of maximin testing in a stability region with given stability factor are described both for finite and infinite
stabilization time.