Stability of positive and monotone systems in partially ordered space. (Russian, English) Zbl 1076.37530
Ukr. Mat. Zh. 56, No. 4, 462-475 (2004); translation in Ukr. Math. J. 56, No. 4, 560-576 (2004).
The author studies properties of dynamical systems, with continuous or discrete time, positive or monotone with respect to a cone in the normed phase space. Conditions for the Lyapunov stability and asymptotic stability are found. In particular, a comparison method is developed for this case which gives also conditions for robust stability of a family of systems.
Reviewer: A. N. Kochubei (Kyïv)
MSC:
| 37L15 | Stability problems for infinite-dimensional dissipative dynamical systems |
| 46B40 | Ordered normed spaces |
| 34C12 | Monotone systems involving ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 47B65 | Positive linear operators and order-bounded operators |
| 47N20 | Applications of operator theory to differential and integral equations |
