Designing reduced-dimension controller of differential-algebraic system by criterion of $\mathrm H_2$-optimization

The problem of designing an $\mathrm H_2$-optimal control was solved for the differentialalgebraic system. The controller is based on the minimal-dimension observer. Solution of the design problem comes to solving two Riccati equations having one the order of the dimension of the “slow” subsystem of the original differential-algebraic system and the other, a reduced order. The resulting controller was represented in the class of ordinary systems, which simplifies its realization. An example of designing an $\mathrm H_2$-optimal controller was given.