Some generalized notions of observability

Generalized state-space systems are a more natural way of describing dynamical behavior than standard state-space systems. Such systems exhibit a much richer observability structure than standard state-space systems. Three notions of observability are defined for generalized state-space systems. In contrast to previous work, regularity is not assumed. Geometric characterization of each type of observability and matrix rank tests for each type of observability are derived