Equivalent transformation and weighted $H_{\mathrm{\infty }}$-optimization of linear descriptor systems

The problem of a generalized type of $H_{\mathrm{\infty }}$-control is investigated for a class of admissible descriptor systems with a non-zero initial vector. A generalized performance measure is used, which characterizes the weighted damping level of external and initial disturbances. A non-degenerate transformation of the system is proposed, which allows to apply known methods for evaluation and the achievement of desired performance measures for conventional lower-order systems. A numerical example of a controlled hydraulic system with three tanks is given.