This article is cited in 10 papers

Construction of the Lyapunov–Krasovskii functionals for some classes of positive delay systems

A. Yu. Aleksandrov

St. Petersburg State University, St. Petersburg, Russia

Abstract: A criterion is established for the diagonal stability of positive linear difference-differential systems with discrete and distributed delay. The problem is studied of existence of a common diagonal Lyapunov–Krasovskii functional for a family of these systems. The approach developed is used to obtain conditions of the absolute stability and estimates of the time of transient processes for nonlinear difference-differential systems with sector type nonlinearities.

Keywords: positive system, distributed delay, Lyapunov–Krasovskii functional, diagonal stability, switched system, estimate of a solution.

UDC: 517.929.4

MSC: 35R30

Received: 15.04.2018

DOI: 10.17377/smzh.2018.59.501

 English version: Siberian Mathematical Journal, 2018, 59:5, 753–762

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