On K-Positivity Properties of Time-Invariant Linear Systems Subject to Discrete Point Lags

• Published in: Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 11; no. 2; pp. 319 - 340
• Main Author: De la Sen, Manuel
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.05.2007; Springer Nature B.V
• Subjects: Control theory; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematical models; Mathematics; Ordinary differential equations; Sciences and techniques of general use; Studies; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Linear system; Differential equation; Differential invariant; Functional equation; Positivity; Delay time; Dynamical system; Delay equation
• ISSN: 1385-1292; 1572-9281
• DOI: 10.1007/s11117-006-2047-5

This paper discusses non-negativity 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 non-negativity and positivity 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 developed by defining cones for the input, state and output spaces of the dynamic system. [PUBLICATION ABSTRACT]