Abstract
One form of the singular systemAx′+Bx=f is considered. The analytic solution, perturbation, and numerical solution of this form are examined. A class of systems which may be transformed into this form without altering these properties is characterized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. K. Brayton, F. G. Gustavson, and G. D. Hachtel, A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas, Proc. IEEE60 (1972), 98–108.
S. L. Campbell,Singular Systems of Differential Equations, Pitman, Marshfield, MA, 1980.
S. L. Campbell,Singular Systems of Differential Equations II, Pitman, Marshfield, MA, 1982.
S. L. Campbell, Consistent initial condition for singular nonlinear systems, Circuits, Systems and Signal Processing2 (1983), 45–55.
S. L. Campbell, Index two linear time varying singular systems of differential equations, SIAM J. Algebraic and Discrete Methods (to appear).
S. L. Campbell, Higher index time varying singular systems, Proceedings IFAC Workshop on Singular Perturbations and Robustness of Control System, Ohrid, Yugoslavia, 1982 (to appear).
S. L. Campbell and C. D. Meyer, Jr.,Generalized Inverses of Linear Transformations, Pitman, Marshfield, MA, 1979.
J. D. Cobb, On the solutions of linear differential equations with singular coefficients, J. Diff. Equations (to appear).
B. A. Francis, Convergence in the boundary layer for singularly perturbed equations, Automatica18 (1982), 57–62.
C. W. Gear, Simultaneous numerical solution of differential-algebraic equations, IEEE Trans. Circuit TheoryCT-18 (1971), 89–95.
C. W. Gear and L. R. Petzold, Differential algebraic systems and matrix pencils, Proceedings of Conference on Matrix Pencils, Pitea, Sweden, March, 1982 (to be published Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, New York.
M. Ikeda, D. D. Siljak, and D. E. White, Decentralized control with overlapping information sets, J. Opt. Theory Appl.34 (1981), 279–310.
M. Ikeda and D. D. Siljak, Generalized decompositions of dynamic systems and vector Lyapunov functions, IEEE Trans. Aut. Cont.AC-26 (1981), 1118–1125.
W. Liniger, Multistep and one-leg methods for implicit mixed differential algebraic systems, IEEE Trans. Circuits SystemsCAS-26 (1979), 755–762.
D. G. Luenberger, Dynamic equations in descriptor form, IEEE Trans Aut. ControlAC-22 (1977), 312–321.
R. W. Newcomb, The semistate description of non-linear time-variable circuits, IEEE Trans. Circuits and SystemsCAS-28 (1981), 62–71.
S. Sastry and O. Hijab, Bifurcation in the presence of small noise, Systems and Control Letters1 (1981), 159–167.
L. M. Silverman, Inversion of multivariable linear systems, IEEE Trans. Aut. ControlAC-14 (1969), 270–276.
R. F. Sincovec, A. M. Erisman, E. L. Yip, and M. A. Epton, Analysis of descriptor systems using numerical algorithms, IEEE Trans. Autom. ControlAC-26 (1981), 139–147.
Author information
Authors and Affiliations
Additional information
Research sponsored by Air Force Office of Scientific Research, Air Force Systems Command, under Grant No. AFOSR-81-0052A. The United States Government is authorized to reproduce and distribute reprints for governmental purposes not with-standing any copyright notation here on.
Rights and permissions
About this article
Cite this article
Campbell, S.L. One canonical form for higher-index linear time-varying singular systems. Circuits Systems and Signal Process 2, 311–326 (1983). https://doi.org/10.1007/BF01599073
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01599073