Design of $H_2$-optimal controllers for time-delay systems. Spectral approach

The problem of $H_2$ optimization of a linear time-invariant system with delays is considered. The design method based on a spectral approach is proposed. The use of such approach for single input problems can greatly simplify the analysis and synthesis of optimal controllers in comparison with “2-Riccati” and LMI methods which are usually applied. Such simplification is highly important in implementing algorithms of adaptive adjustment of control laws for various dynamic objects in the real-time mode due to the possible resource constraints of digital devices that are forming control inputs for dynamic objects and various embedded systems.