Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 25872, 28 pages
Research Article

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

M. De la Sen

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

Received 14 September 2006; Revised 12 March 2007; Accepted 19 March 2007

Academic Editor: Alexander Domoshnitsky

Copyright © 2007 M. De la Sen. 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.


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.