Create LMIs

The function iqclmi facilitates the definition of new LMI constraints. In the present version of the toolbox, this is limited to generating LMIs of the form

    \[JC^TB^TPBC\succcurlyeq JC^TAC+\epsilon I.\]


  • P is a symmetric structured matrix variable defined with the class iqcvar
  • J is the inertia of the LMI (i.e., J=1 and J=-1 mean positive- and negative definite respectively)
  • A is a constant symmetric matrix
  • B is a constant matrix
  • C is a constant matrix (e.g., an annihilator)
  • \epsilon is a small constant enforcing the LMI to be strict (this constant can be modified by changing the property eps in the iqcprob class

Note: It is emphasized that all LMIs can be written in this form. Clearly, this still requires some additional parsing. In future releases the aim is to further mature this.

Specifying LMIs proceeds as follows.

iqcprob=iqclmi(iqcprob,P,J)This generates the LMI

JP\succcurlyeq\epsilon I
iqcprob=iqclmi(iqcprob,P,J,A)This generates the LMI

JP\succcurlyeq JA+\epsilon I
iqcprob=iqclmi(iqcprob,P,J,A,B)This generates the LMI

JB^TPB\succcurlyeq JA+\epsilon I
iqcprob=iqclmi(iqcprob,P,J,A,B,C)This generates the LMI

JC^TB^TPBC\succcurlyeq JC^TAC+\epsilon I

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