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A bound of conservativeness in sampled-data robust stabilization and its dependence on sampling periods
Authors:Yasuaki Oishi
Affiliation:Department of Mathematical Engineering and Information Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
Abstract:This paper investigates conservativeness of the 2-induced norm in a sampled-data robust stabilization problem. Namely, it is shown that possible conservativeness of the 2-induced norm can be bounded by difference between the best achievable performance of time-invariant continuous-time controllers and that of sampled-data controllers. Moreover, this difference is proven to approach zero as a sampling period tends to zero, which means the conservativeness above loses importance when a sampling period is small. These results are important because robust stabilization based on the 2-induced norm is computationally inexpensive compared with robust stabilization based on the non-conservative robust stability index. One key lemma plays an essential role in this paper and it should be interesting independently.
Keywords:Sampled-data control  Robust stabilization  Conservativeness  Sampling period    2-induced norm
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