论文信息 - Index of an implicit time-varying linear differential equation: a noncommutative linear algebraic approach

Index of an implicit time-varying linear differential equation: a noncommutative linear algebraic approach

Abstract An intrinsic definition of the index for implicit linear time-varying differential systems is proposed. This definition relies on linear algebraic techniques over the noncommutative principal ideal ring of nonconstant linear differential operators (noncommutative transfer function or state variable representation). Accordance with the existing definition for constant coefficient linear systems is demonstrated.

[1] Öystein Ore. Formale Theorie der linearen Differentialgleichungen. (Erster Teil). , 1932 .

[2] Michael Patrick. O'Donnell,et al. Theory of rings , 1952 .

[3] R. F. Sincovec,et al. Analysis of descriptor systems using numerical algorithms , 1981 .

[4] R. Tennant. Algebra , 1941, Nature.

[5] Ernst Hairer,et al. The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[6] E. Griepentrog,et al. Differential-algebraic equations and their numerical treatment , 1986 .

[7] B. Malgrange. Équations différentielles à coefficients polynomiaux , 1991 .

[8] P. Cohn. Free rings and their relations , 1973 .

[9] P. M. Cohn,et al. Algebra (2nd edition): volume 3 , by P.M. Cohn. Pp 474. £55. 1990. ISBN 0-471-92840-2 (Wiley) , 1992 .

[10] M. Fliess. Some basic structural properties of generalized linear systems , 1991 .

[11] J. Dieudonné,et al. Les déterminants sur un corps non commutatif , 1943 .

[12] Edward W. Kamen,et al. Representation and realization of operational differential equations with time-varying coefficients , 1976 .