A BOUND OF CONSERVATIVENESS IN SAMPLED-DATA ROBUST STABILIZATION AND ITS DEPENDENCE ON SAMPLING PERIODS

This paper investigates conservativeness of the L-2-induced norm in a sampled-data robust stabilization problem. Namely, it is shown that po ssible conservativeness of the L-2-induced norm can be bounded by the difference between the best achievable performance of time-invariant c ontinuous-time controllers and that of sampled-data controllers. Moreo ver, this difference is proven to approach zero as a sampling period t ends to zero, which means the conservativeness above loses importance when a sampling period is small. These results are important because r obust stabilization based on the L-2-induced norm is computationally i nexpensive compared with robust stabilization based on the non-conserv ative robust stability index. One key lemma plays an essential, role i n this paper and it should be interesting independently. (C) 1997 Else vier Science B.V.