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Aide de Scilab >> Systèmes de Contrôle - CACSD > Factorisation de Systèmes Linéaires > gtild


tilde operation


Gt = gtild(G)
Gt = gtild(G, flag)



either a polynomial or a linear system (syslin list) or a rational matrix


same as G


character string: either 'c' or 'd' (optional parameter).


If G is a polynomial matrix (or a polynomial), Gt=gtild(G,'c') returns the polynomial matrix Gt(s)=G(-s)'.

If G is a polynomial matrix (or a polynomial), Gt=gtild(G,'d') returns the polynomial matrix Gt=G(1/z)*z^n where n is the maximum degree of G.

For continuous-time systems represented in state-space by a syslin list, Gt = gtild(G,'c') returns a state-space representation of G(-s)' i.e the ABCD matrices of Gt are A',-C', B', D'. If G is improper (D= D(s)) the D matrix of Gt is D(-s)'.

For discrete-time systems represented in state-space by a syslin list, Gt = gtild(G,'d') returns a state-space representation of G(-1/z)' i.e the (possibly improper) state-space representation of -z*C*inv(z*A-B)*C + D(1/z).

For rational matrices, Gt = gtild(G,'c') returns the rational matrix Gt(s)=G(-s) and Gt = gtild(G,'d') returns the rational matrix Gt(z)= G(1/z)'.

The parameter flag is necessary when gtild is called with a polynomial argument.


//Continuous time
Gt-horner(G,-s)'   //continuous-time interpretation
Gt-horner(G,1/s)'*s^3  //discrete-time interpretation
G=ssrand(2,2,3);Gt=gtild(G);   //State-space (G is cont. time by default)
clean((horner(ss2tf(G),-s))'-ss2tf(Gt))   //Check

// Discrete-time
Gss=ssrand(2,2,3);Gss('dt')='d'; //discrete-time
Gss(5)=[1,2;0,1];   //With a constant D matrix
Gt2=clean(ss2tf(Gt)); clean(Gt1-Gt2)  //Check

//Improper systems
Gss=ssrand(2,2,3);Gss(7)='d'; //discrete-time
Gss(5)=[z,z^2;1+z,3];    //D(z) is polynomial
G=ss2tf(Gss);Gt1=horner(G,1/z)';  //Calculation in transfer form
Gt=gtild(Gss);    // state-space
Gt2=clean(ss2tf(Gt));clean(Gt1-Gt2)  //Check

See also

  • syslin — définition d'un système dynamique linéaire
  • horner — évaluation d'un polynôme ou d'une fraction rationnelle
  • factors — factorisation réelle de polynômes
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