Parametric optimization of infinite-dimensional systems

The aim of this paper is to present an exact method of evaluating the quadratic performance index for infinite-dimensional systems. Our method relies on solving the Lyapunov operator equation with unbounded operators. For delay — differential systems of the neutral type an explicit construction of the solution to the Lyapunov operator equation is given. The results are illustrated by two examples of the determination of a classical controller setting. An approximation method of evaluating the quadratic performance index is also provided and compared with the exact method.