Estimation of influence and suppression of bounded perturbations in descriptor control systems

Abstract

The necessary and sufficient conditions for existence of dynamic regulators that provide a prescribed estimate of the weighted damping level of bounded disturbances and robust stability of linear descriptor systems are established.
An algorithm for the generalized $H_\infty$-optimization of descriptor systems with controlled and observed outputs as well as a method for finding the worst vectors of external and initial disturbances with respect to a weighted performance criterion are proposed.
The main computational procedures of the algorithm reduce to solving the linear matrix inequalities with additional rank restrictions.
The efficiency of the algorithm is demonstrated by the illustrative example of a descriptor stabilization system with bounded disturbances.