Robust C-controllability and/or C-observability for uncertain descriptor systems with interval perturbations in all matrices

For descriptor systems of the form Ex˙(t)=Ax(t)+Bu(t), y(t)=Cx(t), existing results are mostly for systems with uncertainties in the A matrix only. The case where the E matrix is perturbed renders its robust analysis quite involved and has seldom been touched by researchers. This paper will show that if E, A, B, and G are all interval matrices, the robust controllability and/or observability problems can be solved in terms of the structured singular value p of certain fixed matrices. Necessary and sufficient conditions are given using the structured singular value μ by changing the problem into a robust nonsingularity problem for a class of uncertain matrices