SISO CONTROLLER-DESIGN TO MINIMIZE A POSITIVE COMBINATION OF THE L(2)AND THE H-2 NORMS

We consider the problem of minimizing a given positive linear combinat ion of the l(1) norm and the square of the H-2 norm of the closed loop over all internally stabilizing controllers. The problem is analysed for the discrete-time, SISO, linear time-invariant case. It is shown t hat a unique optimal solution always exists, and can be obtained by so lving a finite-dimensional convex optimization problem with an a prior i determined dimension. It is also established that the solution is co ntinuous with respect to changes in the coefficients of the linear com bination. (C) 1997 Elsevier Science Ltd.