yields the Jordan decomposition of the state-space model ssm.


  • The result is a list {p,jc}, where p is a similarity matrix, and jc is the Jordan canonical form of ssm.
  • The state-space model ssm can be given as StateSpaceModel[{a,b,c,d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
  • continuous-time system
    discrete-time system
  • The transformation , where is the new state vector, and is a similarity matrix that spans the linearly independent eigenvectors of , transforms the system into the Jordan canonical form:
  • w'(t)=TemplateBox[{p}, Inverse].a.p.w(t)+TemplateBox[{p}, Inverse].b.u(t), continuous-time system
    w(k+1)=TemplateBox[{p}, Inverse].a.p.w(k)+TemplateBox[{p}, Inverse].b.u(k),.discrete-time system
  • The new state matrix TemplateBox[{p}, Inverse].a.p is the Jordan canonical form of the old state matrix .
Introduced in 2010