Positivity, robust stability and comparison of dynamic systems

Pages: 1042 - 1051, Issue Special, September 2011

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Alexey G. Mazko - Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka Str., 3, Kyiv, 01601, Ukraine (email)

Abstract: 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.

Keywords:  Monotone system, Positive system, Lyapunov stability, Cone
Mathematics Subject Classification:  Primary: 34D20, 47H07; Secondary: 34C12, 47A50

Received: June 2010;      Revised: April 2011;      Published: October 2011.