This article is cited in 19 papers

The solvability of the initial problem for a degenerate linear hybrid system with variable coefficients

A. A. Shcheglova

Department of Nonlinear Dynamical Systems and Differential Equations, Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia

Abstract: We consider a linear hybrid system with variable coefficients and known mode switching moments under the assumption that matrices at the derivative of the desired vector function are identically degenerate. We obtain the necessary and sufficient conditions for the existence of a piecewise smooth solution (either continuous or not in its definition domain) for the initial problem. We study an equivalent structural form of a nonstationary system of linear differential-algebraic equations with time varying coefficients. We propose a constructive algorithm for obtaining such a form even if the rank of the matrix at the derivative is not constant.

Keywords: hybrid system, differential-algebraic equations, equivalent transformation, solvability, consistent initial data.

UDC: 517.926

Received: 05.11.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:9, 49–61

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