This article is cited in 6 papers

Systems with Lumped Parameters

External bounds and step controllability of the linear interval system

L. T. Ashchepkov

Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia

Abstract: The differential equations describing double-sided bounds of the fundamental matrix of solutions for the linear control system with variable interval coefficients are obtained. Based on those bounds, the controllability problem, i.e., the possibility to transfer the system from a given parallelepiped to another in finite time in the class of step (piecewise constant) controls, is examined. Sufficient conditions of controllability in the form of solvability of an auxilliary linear programming problem are established. This problem results in step control transferring a of system trajectories from an initial parallelepiped to a minimal neighborhood of a final parallelepiped.

PACS: 02.30.Yy

Presented by the member of Editorial Board: V. N. Bukov

Received: 16.01.2007

 English version: Automation and Remote Control, 2008, 69:4, 590–596

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