Optimal induced l1-norm state feedback control

This paper considers state feedback control for linear discrete-time systems to minimize the closed loop l(1)-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 ([10]) and the contractive set algorithm ([7]), 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 l(1)-induced norm achievable by a linear controller is actually achieved by the proposed synthesis approach.