Parametric optimization of a Second Order Time Delay System with a PI-Controller

In the work is posed and solved the parametric optimization problem for second order linear system with delay in control. The control is realised by means of a PI-Controller in the closed loop feedback. It is considered the performance index integral of squared error. The value of the performance index is obtained using of the Lyapunov functional and is equal to the value of the Lyapunov functional at initial function. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper are presented the optimization results for different time delays and for varies damping factors.