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  • Research Article
  • Open Access

About -Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays

Journal of Inequalities and Applications20072007:025872

  • Received: 14 September 2006
  • Accepted: 19 March 2007
  • Published:


This paper discusses nonnegativity and positivity concepts and related properties for the state and output trajectory solutions of dynamic linear time-invariant systems described by functional differential equations subject to point time delays. The various nonnegativities and positivities are introduced hierarchically from the weakest one to the strongest one while separating the corresponding properties when applied to the state space or to the output space as well as for the zero-initial state or zero-input responses. The formulation is first developed by defining cones for the input, state and output spaces of the dynamic system, and then extended, in particular, to cones being the three first orthants each being of the corresponding dimension of the input, state, and output spaces.


  • Differential Equation
  • Time Delay
  • Linear System
  • State Space
  • Related Property


Authors’ Affiliations

Departamento de Electricidad y Electronica, Instituto de Investigación y Desarrollo de Procesos, Facultad de Ciencias, Universidad del País Vasco, Campus de Leioa (Bizkaia), Aptdo. 644 de Bilbao, Bilbao, 48080, Spain


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© M. De la Sen 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.