Mixed l1/H2 control for MIMO systems

In this paper we consider the mixed l₁/H₂ control problem for multiple input-multiple output (MIMO) discrete-time systems. This problem is formulated as minimizing the l₁-norm of a closed-loop transfer matrix while maintaining the H₂-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value respect to changes in the H₂-norm constraint is studied. The existence of the optimal solutions of mixed l₁/H₂ problem is proved. Since the solution of the mixed l₁/H₂ problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization techniques exist. A simulation example shows the effectiveness and feasibility of the proposed results.