## iqc_get_mlmi

Purpose

Retrives the values of matrices $$P$$ , $$A$$, $$B$$, and $$\Xi$$ of the main LMI corresponding to a gain estimation problem

Synopsis

[P,A,B,Sigma,MainLMI]=iqc_get_mlmi;

Description

This program is used for retriving the values of matrices $$P$$, $$A$$, $$B$$, and $$\Xi$$ (where $$\Xi=\Xi_{1}+\Xi_{2}$$) as deﬁned in iqc_gain_tbx optimization problem, provided the optimization problem was found feasible. The matrix MainLMI is the value of

$$\begin{bmatrix} PA+A^{T}P & PB\\B^{T}P & 0\end{bmatrix}+\Xi.$$

Example

Consider the example in section iqc_diag. After the execution of the IQC Toolbox script

>> A=[-8.9130,1.5647; 2.5647,-3.1850];
>> B=eye(2);
>> C=2*eye(2);
>> G=ss(A,B,C,zeros(2));
>> abst_init_iqc
>> f=signal(2);
>> w=signal(2);
>> v=G*(f+w);
>> w==iqc_diag(v);
>> g=iqc_gain_tbx(f,v)

type

>> [P,A,B,S,M]=iqc_get_mlmi

to get the values of matrices $$P$$, $$A$$, $$B$$, and $$\Xi$$. We will have

iqc_gain_tbx