On instability of control systems for a certain class of objects and methods of its elimination

In practice of design of control systems, the cases occur when some of the roots of the transfer function of a controllable object are disposed on the imaginary axis of the complex plane. The optimal controller constructed for such objects, despite its realizability, will not afford the robustness properties in the system. The methods of removal of this phenomenon are given. The comparative estimate of the solution of this problem is provided both in the space of states and in the input-output relations (in the space of operators).