Singular $\mathcal{H}_2$-optimization problems for discrete-time systems

Singular $\mathcal{H}_2$-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular $\mathcal{H}_2$-problems. A parameterization of the set of optimal controllers is given.