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Piecewise linear functions are used in general to ''replace'' a nonlinear function with several local linear functions. The term ''canonical'', in this context, names all representations having the minimum number of parameters. This is very important if you need to work and make calculations in a computer. 

 

Minimal Degenerate Intersection of a PWL function in a three-dimensional domain

We have developed a canonical representation using a simplicial partition, which is the first representation valid in an n-dimensional domain. After that, we developed the foundations for a completely general canonical PWL representation with the elaboration of an explicit representation for a function on a minimal degenerate intersection (this has been proved to be the basic building block in any PWL representation). Currently, we are working in the extension of this result to the case of non-minimal degenerate intersections, which will provide the last step necessary to complete the theory. 

List of publications

  •  P. Julián, ``The Complete Canonical Piecewise--Linear Representation: Functional Form--Part I: Minimal Degenerate Intersections,''  to appear, IEEE Trans. Circuits and Systems, 2001. 

  •  P. Julián, A. Desages, B. D 'Amico, ``Orthonormal High Level Canonical PWL functions with Applications to model reduction,'' IEEE Transactions on Circuits and Systems, vol. 47, No. 5, pp. 702-712, May 2000.

  •  P. Julián, A High Level Canonical Piecewise Linear Representation Using a Simplicial Partition: Theory and Applications, Doctoral Thesis, Department of Electrical Engineering, Universidad Nacional del Sur, Argentina, 1999.

  •  P. Julián, A. Desages, O. Agamennoni, ``High Level Canonical Piecewise Linear Representation Using a Simplicial Partition,'' IEEE Transactions on Circuits and Systems, vol. 46, No. 4, pp. 463-480, April 1999.

  •  P. Julián, J. Guivant, A. Desages, ``A Parametrization of Piecewise linear Lyapunov Functions via Linear Programming,'' International Journal of Control, vol. 72, No. 7/8, pp. 702-715, 1999. Special issue on Multiple models approaches in modelling and control.

  •  P. Julián, M. Jordán, A. Desages, ``Canonical Piecewise Linear Approximation of Smooth Functions,'' IEEE Transactions on Circuits and Systems, vol. 45, No. 5, pp. 567-571, May 1998.