H∞ control of descriptor systems with norm-bounded uncertainties in the system matrices

In this paper the H_∞ control of high index or even non-regular linear descriptor systems with norm-bounded uncertainties in the system matrices is considered. This setup not only includes the possibility to deal with physical parameter uncertainty but also can be used to describe unknown nonlinearities provided they are bounded. The analysis of these uncertain descriptor systems within the closed loop is based on a quadratic H_∞ performance approach. The corresponding analysis result can be re-interpreted in order to also address the controller synthesis problem. The analysis as well as the synthesis result can be stated in form of a parametrized linear matrix inequality