Convex Optimization

In this paper we propose an alternative solution to rl-blodr 1' problems. This altemativeis based upon the idea of transforming the I' problem into an equivalent (in the sense of having the same solution) mixed ll/'Hm problem that can be solved using convex optimieation techniques. The proposed algorithm has the advantage of generating, at each step, an upper bound of the cost that converges uniformly to the optimal cost. Moreover, it allows for easily incorporating frequency and regional pole placement constraints. Finally, it does not require either solving large LP problems or obtaining the zero structure of the plant and computing the so-called zero interpolation and the rank interpolation conditions. The main drawback of this method is that it may suRer from order idation. However, consistent numerical experience shows that the controllers obtained, albeit of high order, are amenable to model reduction by standard methods, with virtually no loss of performance.