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Scilab Help >> Control Systems - CACSD > Control Design > Pole Placement > stabil




F = stabil(A, B, alfa)
K = stabil(Sys, alfa, beta)



square real matrix (nx x nx)


real matrix (nx x nu)

alfa, beta

real or complex vector (in conjugate pairs) or real number.


real matrix (nx x nu)


linear system (syslin list) (m inputs, p outputs).


linear system (p inputs, m outputs)


F=stabil(A,B,alfa) returns a gain matrix F such that A+B*F is stable if pair (A,B) is stabilizable. Assignable poles are set to alfa(1),alfa(2),.... If (A,B) is not stabilizable a warning is given and assignable poles are set to alfa(1),alfa(2),.... If alfa is a number all eigenvalues are set to this alfa (default value is alfa=-1).

K=stabil(Sys,alfa,beta) returns K, a compensator for Sys such that (A,B)-controllable eigenvalues are set to alfa and (C,A)-observable eigenvalues are set to beta.

All assignable closed loop poles (which are given by the eigenvalues of Aclosed=h_cl(Sys,K) are set to alfa(i)'s and beta(j)'s.


// Gain:
spec(A) //2 controllable modes 2 unstable uncontrollable modes
//and one stable uncontrollable mode
spec(A+B*F) //the two controllable modes are set to -1.
// Compensator:
Sys=ssrand(3,2,5,list('st',2,3,3)); //3 outputs, 2 inputs, 5 states
//2 controllables modes, 3 controllable or stabilizable modes.
K=stabil(Sys,-2,-3);  //Compensator for Sys.
spec(h_cl(Sys,K))   //K Stabilizes what can be stabilized.

See also

  • st_ility — stabilizability test
  • contr — controllability, controllable subspace, staircase
  • ppol — pole placement
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Last updated:
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