| Singular systems of differential equations arise in many areas of science and technology, including electro-mechanical systems, electronic circuits, chemical and biological reactors, and fluid flow systems. In this thesis, two classes of singular nonlinear systems are considered; namely, (i) singularly perturbed systems, and (ii) generalized systems, or descriptor, or differential-algebraic systems. H2 and H∞ techniques for state estimation of these classes of systems are developed, and sufficient conditions for the solvability of the problems in terms of Hamilton-Jacobi equations are presented. Both continuous-time and discrete-time systems are considered, and examples are presented to show the usefulness of the results. |
