On state-space realization of Bézout factorizations in singular systems. (English) Zbl 1106.34035

For singular systems of the form \[ E\dot x(t)= Ax(t)+ Bu(t),\quad y(t)= Cx(t), \] the authors establish a new Bézout factorization of the transfer function matrix \(G(s)\) and of the causal reduced order stabilizing compensator \(K(s)\).
Compared with previous analogous results, the advantage of the present result is that all the transfer function matrices appearing in the Bézout factorization are proper and stable.


34H05 Control problems involving ordinary differential equations
93B52 Feedback control
34A09 Implicit ordinary differential equations, differential-algebraic equations