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Scilab Help >> Control Systems - CACSD > Linear Analysis > Controllability Observability > ctr_gram

ctr_gram

controllability gramian

Syntax

Gc = ctr_gram(sl)
Gc = ctr_gram(A, B)
Gc = ctr_gram(A, B, dom)

Arguments

A,B

two real matrices of appropriate dimensions

dom

character string ('c' (default value) or 'd')

sl

linear system, syslin list

Description

Controllability gramian of (A,B) or sl (a syslin linear system).

dom character string giving the time domain : "d" for a discrete time system and "c" for continuous time (default case).

Examples

A=diag([-1,-2,-3]);B=rand(3,2);
Wc=ctr_gram(A,B)
U=rand(3,3);A1=U*A/U;B1=U*B;
Wc1=ctr_gram(A1,B1)    //Not invariant!

See also

  • equil1 — balancing (nonnegative) pair of matrices
  • obs_gram — observability gramian
  • contr — controllability, controllable subspace, staircase
  • cont_mat — controllability matrix
  • cont_frm — transfer to controllable state-space
  • contrss — controllable part
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with contributors 		Last updated:
Mon Jan 03 14:23:25 CET 2022