invrse

this function compute the inverse restricted system equivalence of a descriptor system (E, A, B)

Calling Sequence

[Ee, Ae, Be]=invrse(E,A,B)
[Ee, Ae, Be]=invrse(E,A,B, lambda)

Parameters

E, A, B:: Matrices of descriptor system, E singular and pair (E, A) regular.
Ee, Ae, Be:: Matrices of equivalent inverse r.s.e system
lambda: Escalar that multiplies lamda*E

Description

Consider the descriptor linear system (E, A, B) with pair (E, A) regular, then exist a matrix Q satisfying

Q=(lamdaE-A)^{-1}

lamda is a scalar, then

Ee=QE

Ae=QA

Be=QB

Ce=C

Examples

// Descriptor system
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];
B=[ 0 0; -0.0856  0.01; 0 0; 0 1];
C=[1 1 0 1; 0 0 1 1;0 0 1 0];

// Compute the inverse r.s.e of (E,A,B),
 [Ee, Ae, Be]=invrse(E,A,B)
// Inverse r.s.e considering lambda=5
[Ee, Ae, Be]=invrse(E,A,B,5)

Authors

Francisco Ronay López Estrada

Bibliography

Duan, G.-R. Gao, D. Y. adn R. W. Ogden, (210). Analysis and Desing of Descriptor Linear Systems. Edit. Springer.

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