Abstract—It is well known that important problems such as structured H 2 control synthesis or simultaneous stabilization have no polynomial time solution in general. The underlying BMI problem can’t be reduced to an LMI. The recent description of dilated LMI’s under the continuous time setting however, enables new characterizations for such problems allowing interesting additional degrees of freedom. Based on it, a novel coordinate-descent iterative algorithm is proposed as an efficient alternative to existing ones, in order to approach the solution of the problems considered. The relevance of the approach is illustrated with several numerical examples. I. INTRODUCTION ILATED LMI’s [1] are often regarded as a powerful tool to establish new characterizations for control analysis and synthesis problems, even in the continuous time setting [2]. Dilated LMI’s presented in [3] are shown to be efficient when dealing with mutiobjective control problems since they enable to associate distinct Lyapunov matrices to different objectives. This paper aims to show some other advantages of dilated LMI’s especially when dealing with the H 2 control under structural constraints. An important problem in control arises when a specific structure on the overall control scheme is considered, especially when dealing with complex or distributed systems [4]. This structure often depends on the structure of the system itself, subdivided in subsystems. It also depends on the signals accessible for measure and the authority on actuation variables of each separated controller included in the global desired controller. Finding an H 2 controller under structural constraints is a difficult optimization problem. Except in some particular cases, for example when the controller/plant structure satisfies the so called quadratic invariance property [5], [6] the problem is indeed non convex. Even if many sub- optimal numerical procedures (see for example [7]-[13]) have been developed to reduce the conservatism and the M. Yagoubi and P. Chevrel are with the Ecole des Mines de Nantes, 4 rue Alfred Kastler, 44307 Nantes, France (corresponding author phone: +(33)-251858327; fax: +(33)-251858349; e-mail: myagoubi@emn.fr). They are also with IRCCyN (UMR CNRS 6957), BP 92101, 44321 Nantes Cedex 3, France. computational time for related problems, looking for more and more efficient algorithm remains an important and challenging problem. Using new characterizations based on dilated LMI’s for some structured control problems, a novel coordinate- descent iterative numerical procedure is proposed in this paper. In particular, the H 2 control under structural constraints problem is considered in the continuous time setting. The algorithm developed is used to compute local optimal solutions. A decomposition in consecutive sub- problems of the initial problem enable to improve the numerical results obtained. The paper is organized as follows. Leaning on the dilation lemma, section 2 recalls the definitions and characterizations of the stability and H 2 structured control problems considered. In section 3, a new iterative procedure is proposed to approach the solution of such problems. In section 4, some examples broadly studied in the literature are studied. Finally numerical test-examples whose global optimum is known are constructed and used for test in section 5. The conclusion takes place in section 6. II. SOME DEFINITIONS AND PROBLEMS The notations below will be used through the paper. ( ) T sym A A A and T A B A B C B C denotes the direct product of matrices 1 1 1 1 1 u y u y n n n n In this paper, we consider the continuous linear time- invariant (LTI) system with state-space representation (1) 22 21 2 12 11 1 2 1 22 21 12 11 : D D C D D C B B A s P s P s P s P s P (1) u w x D D C D D C B B A y z x 22 21 2 12 11 1 2 1 with 11 22 0 D D . T zw denotes the closed-loop transfer matrix between the Structured H 2 Controller Synthesis via a dilated LMI Based Algorithm M. Yagoubi and P. Chevrel D Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005 WeC05.3 0-7803-9568-9/05/$20.00 ©2005 IEEE 5746