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Piecewise linear resistive networks with unique solutions

Piecewise linear resistive networks with unique solutions

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  • Author(s): V.C. Prasad 1  and  V. Prem Prakash 2
    • View affiliations
    • Affiliations: 1: Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India
      2: Department of Electrical Engineering, Faculty of Engineering, Dayalbagh Educational Institute, Agra, India
  • Source: Volume 22, Issue 2, 16 January 1986, p. 90 – 91
    DOI:  10.1049/el:19860061 , Print ISSN 0013-5194, Online ISSN 1350-911X
© The Institution of Electrical Engineers
Published

New conditions for the existence of unique solutions of piecewise linear resistive networks are presented. They require that certain submatrices of unbounded regions are all positive definite or all negative definite. The applicability of these conditions can be enhanced by using a suitable transformation.

Inspec keywords: nonlinear network analysis; matrix algebra; piecewise-linear techniques

Other keywords: Jacobian determinant; homeomorphism; transformation; unique solutions; nonlinear network analysis; piecewise linear resistive networks; unbounded regions; submatrices

Subjects: Nonlinear network analysis and design; Algebra

References

    1. 1)
      • V.C. Prasad , P.B.L. Gaur . Sufficient conditions for global homeomorphism of piecewise linear functions. Electron. Lett. , 335 - 337
    2. 2)
      • J.M. Ortega , W.C. Reinbolt . (1970) , Interative solutions of nonlinear equation in several variables.
    3. 3)
      • T. Ohtsuki , T. Fujisawa , S. Kumagai . Existence theorems and a solution algorithm for piecewise linear resistor networks. SIAM J. Math. Anal. , 69 - 99
    4. 4)
      • T. Fujisawa , E.S. Kuh . Piecewise linear theory of nonlinear networks. SIAM J. Appl. Math. , 307 - 327
    5. 5)
      • M.J. Chein . Piecewise linear theory and computation of solutions of homeomorphic resistive networks. IEEE Trans. , 118 - 127
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