Mathematics of Control, Signals and Systems

, Volume 18, Issue 2, pp 147–186

A lattice approach to analysis and synthesis problems


DOI: 10.1007/s00498-005-0159-2

Cite this article as:
Quadrat, A. Math. Control Signals Syst. (2006) 18: 147. doi:10.1007/s00498-005-0159-2


Within a lattice approach, the purpose of this paper is to give general necessary and sufficient conditions for internal stabilizability and for the existence of (weakly) left-/right-/doubly coprime factorizations of multi input multi output linear systems. These results extend the ones recently obtained in [24] for single input single output systems. In particular, combining these results with the one obtained in [3, 13], we prove that every internally stabilizable multidimensional system admits doubly coprime factorizations, solving Lin's conjecture [17, 18].


Fractional representation approachLattice approachInternal stabilizability(weakly) left-/right-/doubly coprime factorizationLin's conjectureMultidimensional systemsModule theory

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.INRIA Sophia AntipolisCAFE projectSophia Antipolis CedexFrance