DUALITY, OBSERVABILITY, AND CONTROLLABILITY FOR 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) was recently developed. Neither E nor C were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the form E(t)x'(t) + F(t)x(t) = f(t).