Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article About K-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 25872 28 pages doi 2007 25872 Research Article About K-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays M. De la Sen Received 14 September 2006 Revised 12 March 2007 Accepted 19 March 2007 Recommended by Alexander Domoshnitsky 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. 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. 1. Introduction Positive systems have an important relevance since the input state and output signals in many physical or biological systems are necessarily positive 1-19 . Therefore important attention has been paid to such systems in the last decades. For instance an hydrological system composed of a set of lakes in which the input is the inflow into the upstream lake and the output is the outflow from the downstream lake is externally positive system since the output is always positive under a positive input 8 . Also hyperstable single-input single-output systems are externally positive since the .
