Regularizable singular systems: a complete system of invariants

  • Authors:

  • M. Isabel García-Planas;A. Díaz

  • Affiliations:

  • Departament de Matemática Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemática Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain

  • Venue:
  • ACC'08 Proceedings of the WSEAS International Conference on Applied Computing Conference
  • Year:
  • 2008

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Abstract

Let (E, A, B, C) be a quadruple of matrices with E, A ∈ Mn(C), B ∈ Mn×m(C), C ∈ Mp×n(C) representing a singular time-invariant linear system, Ex = Ax + Bu, y = Cx. In this paper we present a collection of invariants for singular systems in terms of ranks of certain matrices, that permit us to reduce the system in a canonical form in such a way that the system is decomposed in following five independent subsystems: i) controllable and observable system, ii) controllable non observable system, iii) observable non controllable system, iv) Jordan system v) completely singular system.