FundMatrix

This funtion find the Laurent Expansion coefficients of a pair pencil (E, A).

Calling Sequence

[Phim, Phip]=FundMatrix(E,A)
[Phim, Phip,k]=FundMatrix(E,A)

Parameters

E:: Singular matrix // single line description of each parameter.
A:: A matrix // parameter name and description must be
Phim:: Laurent expansion coefficients for k=1,2,... k<0
Phip:: Laurent expansion coefficients for k=1,2,... k>=0
k:: Nilpotence Index of Kronecker-Weistrauss transformation

Description

This function find the Laurent Expansion coefficients. Add an empty comment line to format the text into separate paragraphs.

Phi(s)=(sE-A)^-1=Phi_{-k}s^{k-1}+...+Phi_{-2}s+Phi_{0}s^{0}+Phi_{1}s^{-1}+...+\Phi_{k}s^{-k-1}

where Phi_{-1} and Phi_{0} are computed using a modified Drazin inverse

Examples

// Descriptor system
//for more details look into FundMatrix.sci in macros path
E=[1 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0];
A=[-0.8775 0 0.526 -0.0274;
    -5.8500  -0.5 0.1481 0.0026; 
    0      0.5   -1     0.2;
    0      2.6522  -0.274  -2];

// Compute the Laurent Expansion Coefficients
[Phim, Phip,h]=FundMatrix(E,A) // examples of use

Authors

Francisco Ronay López Estrada

References

Karampetakis, N. P. (2003). On the discretization of singular systems. IMA Journal of Mathematical Control and Information. Vol. 21, pp. 223-242

Lewis, F. L. (1990). On the Analysis of Discrete Linear Time-Invariant Singular Systems. IEE Transactions on Automatic Control.Vol. 35, pp. 506-511

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