Generalized L1-optimization problem: reduction to a finite-dimensional convex minimization

The minimax compensator design problem is stated for a MIMO dynamic plant with a convex set of disturbances in l^∞ space. The performance index is a convex function of the output. This is a generalization of the l¹-optimal compensator design problem. The main result is a reduction of the problem to a convex minimization problem in a modified state-space of the system plant+measurement. The last problem can be easily solved by various methods including gradient algorithms. The reduction algorithm is the most complex part of the computations. It can be done on the basis of dynamic programming approach