Robust controllability for linear uncertain descriptor systems

In this paper, under assumptions that the linear nominal descriptor system is regular and controllable, some sufficient conditions are proposed to preserve the assumed properties when both structured (elemental) and unstructured (norm-bounded) parameter uncertainties are added into the nominal descriptor system. Besides, another sufficient conditions are also presented to preserve the assumed properties for a class of linear descriptor systems having structured uncertainties in the structure information matrix as well as having both structured and unstructured parameter uncertainties in the system matrix and the input matrix simultaneously. The corresponding results for the dual observability robustness problems are straightforward extensions. Three numerical examples are given to illustrate the applications of the proposed sufficient conditions, and it is shown that the proposed sufficient conditions could be less conservative than the existing ones reported recently in the literature.