Descriptor Variable and Generalized Singularly Perturbed Systems: A Geometric Approach

Abstract : Existing results in descriptor variable theory are interpreted geometrically. New results are obtained concerning linear feedback and pole placement in such systems. Descriptor variable systems are viewed as limits of singularly perturbed systems. It is shown that some important singularly perturbed systems cannot be treated effectively with standard techniques. Hence, a generalized class of singularly perturbed systems is considered. A geometric decomposition that preserves continuity about the singular point is derived. Conditions are presented under which the solution of a singularly perturbed system converges with the parameter. Miscellaneous structural properties are established with applications to the quadratic regulator problem. (Author)