Weighted estimation of damping of the limited perturbations in descriptive discrete control systems

Abstract

We establish necessary and sufficient conditions of the upper bounds for the performance criteria of linear discrete-time descriptor systems characterizing the weighted damping level of external and initial disturbances.
These conditions require to solve linear matrix equations (LMI).
The technique of the generalized $H_\infty$-optimization of the descriptor systems with controlled and observed outputs as well as a method for finding the worst vectors of the external and initial perturbations with respect to the weighted quality criterion are proposed.
An illustrative example of a discrete-time descriptor control system with perturbations is given.