Evaluation of the Weighted Level of Damping of Bounded Disturbances in Descriptor Systems

We establish necessary and sufficient conditions for the realization of the upper bounds in the performance criteria for linear descriptor systems characterizing the weighted level of damping of the external and initial disturbances. The verification of these conditions is reduced to the solution of matrix equations and inequalities. The main statements are formulated with an aim of their subsequent application in the problems of robust stabilization and H ∞ -optimization of descriptor control systems.