On stabilization of linear systems by delayed feedback

An output feedback control problem is considered, namely, the stabilization problem for a linear differential second-order system by a linear feedback control that does not depend on the values of the derivatives of the state functions. A method based on the using of the artificial delay in the control structure has been studied. It is also possible to take into account the information lag in the control loop. In this case, control problem reduces to solving of some linear matrix inequalities. The form of the equations is convenient for describing the motions of mechanical systems. The classical problem of controlling an inverted pendulum is studied to test the method, the influence of the delay on the stabilizing control properties was studied, and a comparison was done of some indicators with a control of a similar structure which was constructed by another method.