MR2332076 Pham Huu Anh NGOC, Toshiki NAITO and Jong Son SHIN Pham Huu Anh NGOC, Toshiki NAITO and Jong Son SHIN Characterizations of Positive Linear Functional Differential Equations Funkcialaj Ekvacioj. Serio Internacia 50 2007 1--17 http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-1/50_1.pdf http://www.ams.org/mathscinet-getitem?mr=MR2332076 In this paper, we first prove that if a linear neutral functional differential equation is positive then it must degrade into a linear functional differential equation of retarded type. Then, we give some explicit criteria for positive linear functional differential equations. Consequently, we obtain a novel criterion for exponential stability of positive linear functional differential equations. Linear functional differential equation, Positive system, Stability. Primary 34K06; Secondary 93D05. 50-1 2007 Characterizations of Positive Linear Functional Differential Equations Pham Huu Anh NGOC, Toshiki NAITO and Jong Son SHIN Pham Huu Anh NGOC, Toshiki NAITO and Jong Son SHIN 1 Berman, A.; Plemmons, R. J. Nonnegative Matrices in the Mathematical Sciences Acad. Press, New York 1979 MR0544666
2 Bernshtein, S. N. A demonstration of the Weierstrass theorem based on the theory of probability The Mathematical Scientist 29 2004 127-128 MR2102260
3 Bliman, P. A. LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov-Krasovskii functionals Systems & Control Letters 43 2001 263-274 MR2007926
4 Bliman, P. A. From Lyapunov-Krasovskii functionals for delay-independent stability to LMI conditions for $\mu$-analysis, Advances in time-delay systems Lect. Notes Comput. Sci. Eng., 38, Springer, Berlin 2004 75-85 MR2087185
5 Diekmann, O.; van Gils, S. A.; Verduyn Lunel, S. M.; Walther. H. O. Delay Equations Functional-, Complex- and Nonlinear Analysis, Springer-Verlag, New York 1995 MR1345150 6 Farina, L.; Rinaldi, S. Positive Linear Systems Theory and Applications, John Wiley and Sons, New York 2000 MR1784150 7 Hale, J. Theory of Functional Differential Equations Acad. Press, New York 1977 MR0508721
8 Hinrichsen, D.; Son, N. K. $\mu$-analysis and robust stability of positive linear systems Appl. Math. and Comp. Sci. 8 1998 253-268 MR1635786
9 Hinrichsen, D.; Son, N. K.; Ngoc, P. H. A. Stability radii of positive higher order difference systems Systems Control Letters 49 2003 377-388
10 Horn, R. A.; Johnson, C. R. Matrix Analysis Cambridge University Press, Cambridge 1993 MR1084815 11 Luenberger, D. G. Introduction to Dynamic Systems, Theory, Models and Applications J. Wiley, New York 1979
12 Ngoc, P. H. A. Strong stability radii of positive linear time-delay systems International Journal of Robust and Nonlinear Control 15 2005 459-472 MR2146322
13 Ngoc, P. H. A.; Son, N. K. Stability radii of positive linear difference equations under affine parameter perturbations Applied Mathematics and Computation 134 2003 577-594 MR1932440
14 Ngoc, P. H. A.; Son, N. K. Stability radii of linear systems under multi-perturbations Numer. Funct. Anal. Optim. 25 2004 221-238 MR2072066
15 Pazy, A. Semigroups of Linear Operators and Applications to Partial Differential Equations Springer-Verlag, Berlin 1983 MR0710486
16 Son, N. K.; Hinrichsen, D. Robust stability of positive continuous time systems Numer. Funct. Anal. Optim. 17 1996 649-659 MR1404841
17 Son, N. K.; Ngoc, P. H. A. Stability radius of linear delay systems in Proceedings of the American Control Conference, San Diego, California, June 1999 1999 815-816
18 Son, N. K.; Ngoc, P. H. A. Robust stability of positive linear time delay systems under affine parameter perturbations Acta Mathematica Vietnamica 24 1999 353-372 MR1735120
19 Son, N. K.; Ngoc, P. H. A. Robust stability of linear functional differential equations Advanced Studies in Contemporary Mathematics 3 2001 43-59 MR1840653
20 Rudin, W. Real and Complex Analysis McGraw-Hill, New York 1987 MR0924157