This article is cited in 6 papers

Linear Systems

On the superstability of an interval family of differential-algebraic equations

A. A. Shcheglova

Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033 Russia

Abstract: We consider an interval family of differential-algebraic equations (DAE) under assumptions that guarantee the coincidence of the structure of the general solution of each of the systems in this family with the structure of the general solution of the nominal system. The analysis is based on transforming the interval family of DAE to a form in which the differential and algebraic parts are separated. This transformation includes the inversion of an interval matrix. An estimate for the stability radius is found assuming the superstability of the differential subsystem of nominal DAE. Sufficient conditions for the robust stability are obtained based on the superstability condition for the differential part of the interval family.

Keywords: differential-algebraic equation, interval coefficients, arbitrarily high unsolvability index, robust stability, superstability.

Presented by the member of Editorial Board: P. S. Shcherbakov

Received: 02.09.2019
Revised: 11.02.2020
Accepted: 09.07.2020

DOI: 10.31857/S0005231021020045

 English version: Automation and Remote Control, 2021, 82:2, 232–244

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