This article is cited in 2 papers

On the extensibility of solutions of nonautonomous quadratic differential systems

E. N. Khailov^a, E. V. Grigorieva<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Texas Woman's University, Denton

Abstract: The extensibility of solutions of a nonautonomous quadratic differential system is considered. Sufficient conditions are established for the existence of solutions of the system on a given closed interval. Corresponding examples of the Riccati equation are presented. The results are applied for the estimation of the number of switchings of piecewise constant controls corresponding to boundary points of the attainable set of a nonlinear control system that describes a two-stage process of a biological treatment of sewage.

Keywords: nonautonomous quadratic differential system, extensibility of solutions, differential inequality, Chaplygin's theorem.

UDC: 517.977.1

Received: 13.06.2013

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