l(1)-optimal control for multirate systems under full state feedback

This paper considers the minimization of the em-induced norm of the closed loop in linear multirate systems when full state information is available f or feedback. A state-space approach is taken and concepts of viability theo ry and controlled invariance are utilized. The essential idea is to constru ct a set such that the state may be confined to that set and that such a co nfinement guarantees that the output satisfies the desired output norm cond itions. Once such a set is computed, it is shown that a memoryless nonlinea r controller results, which achieves near-optimal performance. The construc tion involves the solution of several finite linear programs and generalize s to the multirate case earlier work on linear time-invariant (LTI) systems .