Optimal induced l1-norm state feedback control

This paper considers state feedback control for linear discrete-time systems to minimize the closed loop l¹ induced norm. A generalized bounded real inequality (GBRI) is presented as a sufficient condition to establish a norm bound. Using an algorithm similar to the invariant kernel algorithm and the contractive set algorithm, state feedback synthesis to satisfy GBRI is reduced to a linear programming problem and is numerically tractable. If the problem is feasible, our algorithm gives a polyhedral set that induces a closed loop Lyapunov function and also provides feasible control laws. An example is given for which the optimal l¹-induced norm achievable by a linear controller is actually achieved by the proposed synthesis approach