COMPUTATION OF D, G SCALING

MATRICES AT TWO FREQUENCIES

3.1 THE LMI PROBLEM

Let the complex matrices Mi = M==i ) and M2 = M(==( . Let A a structured model perturbation. The issue is to find the minimal positive value of scalar (3, for which there exist scaling matrices A A A and G Є G satisfying:

MlDM + j(GM – M*G) < (32D

М2 DM2 + j{GM2 – M%G) < /32D (10.6)

This is a well posed generalized eigenvalue problem, which consists in finding the minimal value of /3 satisfying A(D, G) < /3213(D), with:

and:

Remark: when comparing the above LMI problem with the one asso­ciated to the mixed /j, upper bound of (Fan et al., 1991) (see equation

(10.1) ), the number of constraints is increased, but the number of op­timization parameters is the same.