$\mathcal H_2$-optimization of time-delayed sampled-data systems on the basis of the parametric transfer matrix method

A solution to the $\mathcal H_2$-optimization problem for multi-input-multi-output sampled-data system with delay is presented on the basis of the parametric transfer matrix concept. A procedure is developed for design of the optimal controller by means of factorization and separation of real rational matrices. Some qualitative properties of the $\mathcal H_2$-optimal system are established, which are useful for applications. In particular, it is proved that there is a set of fixing poles of continuous-time elements of the system, and performance of the optimal system is limited because of them. A constructive algorithm is given for determination of the set of fixing poles.