Observability of Linear Time-Varying Descriptor Systems

A characterization of observability for linear time-varying descriptor systems $E( t )x' ( t ) + F ( t ) x ( t ) = B (t) u (t), y ( t ) = C ( t ) x ( t )$, is given. E is not required to have constant rank. The characterization is designed to reduce symbolic computation and has potential advantages even when E is nonsingular. It is also shown that all observable analytic descriptor systems are smoothly observable even if they are not uniformly observable. Finally, the external behavior of time-varying descriptor systems is characterized.