Duality, observability, and controllability for linear time-varying descriptor systems

Campbell, S. L., Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 and Terrell, W. J. (1991) Duality, observability, and controllability for linear time-varying descriptor systems. Circuits Systems and Signal Processing, 10 (4). pp. 455-470. ISSN 0278-081X doi: 10.1007/BF01194883

Abstract/Summary

A characterization of observability for linear time-varying descriptor systemsE(t)x(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC 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 formE(t)x(t)+F(t)x(t)=f(tt).