# American Institute of Mathematical Sciences

2011, 2011(Special): 1042-1051. doi: 10.3934/proc.2011.2011.1042

## Positivity, robust stability and comparison of dynamic systems

 1 Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka Str., 3, Kyiv, 01601, Ukraine

Received  June 2010 Revised  April 2011 Published  October 2011

We study generalized classes of positive and monotone dynamic systems in a partially ordered Banach space. Using results from the nonlinear operators theory, we establish new algebraic conditions for stability of equilibrium states of a class of monotone-type di fferential and diff erence systems. Conditions for the positivity and absolute stability of diff erential systems with delay are proposed. Using new technique for constructing the invariant sets of diff erential systems, we generalize known positivity conditions for linear and nonlinear diff erential systems with respect to typical classes of cones. In addition, we generalize the comparison principle for a finite set of diff erential systems and formulate robust stability conditions for some families of diff erential systems in terms of cone inequalities.
Citation: Alexey G. Mazko. Positivity, robust stability and comparison of dynamic systems. Conference Publications, 2011, 2011 (Special) : 1042-1051. doi: 10.3934/proc.2011.2011.1042
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