Inverse matrix definition of matrix variable

[國住勇太]

We are currently trying to model a system using LMI, and at that time we need to define matrix variables and calculate using inverse matrix assuming that it is a regular matrix.

However, in the matrix variable definition as below, it is not possible to define for  regular matrix. so the following error (red part) error will be displayed.

I'd like to overcome this error and lead the solution of the matrix variable by LMI, but if you have a solution please let me know.

thank you.

Hc = sdpvar(3,3,'symmetric')                                       ;

Ec = sdpvar(3,3,'symmetric')                                       ;

 

LMI_Ec = Ec                                                        ;

LMI_1  = Hc-X10M*inv(Ec)*X10M'                                     ;

※X10Mは3行3列の定数行列

??? 未定義の関数またはメソッド 'inv' (タイプ 'sdpvar' の入力引数)。

 エラー ==> LMIact at 181

LMI_1  = Hc-X10M*inv(Ec)*X10M’   

[Johan Löfberg]

You will have to come up with a better model which doesn't involve an inverse of decision variables, through clever variable changes, congruence and Schur complements etc. For instance, if you want LMI_1>=0, you have a prime candidate for a Schur complement