Brief note on the variation of constants formula for fuzzy differential equations

  • Authors:

  • Phil Diamond

  • Affiliations:

  • Department of Mathematics, The University of Queensland, Brisbane, Qld, Australia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2002

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Abstract

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution.