On the Monotonicity of Solutions of Nonlinear Systems with Respect to the Initial Conditions

Author:

Rodina L. I12,Voldeab M. S1

Affiliation:

1. Vladimir State University, Vladimir, 600000, Russia

2. National University of Science and Technology “MISiS”, Moscow, 119049, Russia

Abstract

We consider the autonomous system of differential equations x˙=f(x) and the solution φ(t,x) of this system with the initial condition φ(0,x)=x. Sufficient conditions for the following monotonicity property of solutions with respect to the initial conditions are obtained: if x(0)∈Rn и y(0)∈Rn and x(0)≤\linebreak≤y(0),, then φ(t,x(0))≤φ(t,y(0)) for all t≥0. This property is used to study the problem of almost surely estimating the average time gain for systems with random parameters.

Publisher

The Russian Academy of Sciences

Reference12 articles.

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4. Zaslavsky B.G. Eventually nonnegative realization of difference control systems // Dynamical Systems and Related Topics. Adv. Ser. Dynam. Systems. V. 9. New Jersey, 1991. P. 573-602.

5. Angeli D., Sontag E.D. Monotone control systems // IEEE Trans. Automat. Control. 2003. V. 48. № 10. P. 1684-1698.

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