|State-space Realization and Generalized Popov Belevitch Hautus Criterion for High-order Linear systems—The Singular Case
Guang-Ren Duan* and Ya-Jun Gao
International Journal of Control, Automation, and Systems, vol. 18, no. 8, pp.2038-2047, 2020
Abstract : In this paper, based on the inverse of block companion matrix pencils associated with matrix polynomials, a first-order state-space realization in descriptor system form for a general high-order linear system is derived. An
important feature of the proposed realization is that it allows the high-order linear system to be singular. While in the case that the high-order system is nonsingular, two realizations in normal state-space system forms are directly deduced. With the help of the proposed realization, a generalized Popov Belevitch Hautus (PBH) criterion for highorder systems is then established in terms of the original system matrix polynomials. Examples are studied which well demonstrate the proposed theories.
Companion matrices, continuous-time systems, discrete-time systems, high-order systems, PBH criterion, system realizations.