A design method of multivariable PID controllers that satisfy the performance index of the standard Hoc control problem and linear constraints on the control structure is proposed. Nonconvex/convex matrix inequalities obtained from the Hoc, norm condition for each frequency are approximated by linear matrix inequalities, respectively. A sequence of PID gains is obtained by solving a feasibility problem of the linear matrix inequalities starting from a stabilizing PID gain iteratively. The PID gain converges to a local optimal solution and the sequence of the H-infinity norm bound is monotonically nonincreasing. (c) 2005 Elsevier Ltd. All rights reserved.