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C. Tischendorf (1994)
On the stability of solutions of autonomous index-I tractable and quasilinear index-2 tractable DAEsCircuits, Systems and Signal Processing, 13
J. Vlach, K. Singhal (1983)
Computer Methods for Circuit Analysis and Design
Differential Equations, Vol. 40, No. 1, 2004, pp. 50–62. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 1, 2004, pp. 47–57. Original Russian Text Copyright c 2004 by Shcheglova, Chistyakov. ORDINARY DIFFERENTIAL EQUATIONS Stability of Linear Di erential-Algebraic Systems A. A. Shcheglova and V. F. Chistyakov Institute for System Dynamics and Control Theory, Siberian Division, Russian Academy of Sciences, Irkutsk, Russia Received June 18, 2002 1. INTRODUCTION In the present paper, we consider linear ordinary di erential systems A(t)x (t)+ B(t)x(t)= f (t);t 2 T =[0; +1); (1) where A(t)and B(t)are n n matrix functions, x(t) is the unknown n-vector function, and f (t) is a given n-vector function. We assume that detA(t) 0, t 2 T . Systems of ordinary di erential equations with everywhere degenerate matrix function multiplying the derivative of the unknown vector function are referred to as di erential-algebraic systems. Such systems arise in modeling complex electronic circuits [1] as well as other elds [2]. Di erential-algebraic systems have a complicated internal structure, whose complexity can be characterized by a positive integer r n referred to as the index of a system and measuring the extent to which the system is unsolved for the
Differential Equations – Springer Journals
Published: Oct 18, 2004
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