A solution to MIMO 4-block l1 optimal control problems via convex optimization

Proposes an alternative solution to 4-block l¹ problems. This alternative is based upon the idea of transforming the l ¹ problem into an equivalent (in the sense of having the same solution) mixed l¹/H_∞ problem that can be solved using convex optimization 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 suffer from order inflation. 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