A search method for a fixed-order controller of H2/H∞ control problems

In this paper, a search method for fixed order controllers that satisfy H₂/H_∞ control problems is studied. Since this problem can be reduced to a static output control problem, we give a numerical method for finding a static output feedback gain that makes H₂ norm performance index smaller subject to an H_∞ norm constraint. This method searches for a solution of bilinear matrix inequalities whose variables are Lyapunov matrices and the controller gain matrix. This method is a descent method in the controller gain space where the feasible direction of the gain is computed by solving an linear matrix inequality and then a minimum point in the direction is obtained by a line search. By iterating this procedure, the value of the H₂ cost function decreases monotonically while the H_∞ constraint is being satisfied.