17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper TuA09.4

Hagiwara, Tomomichi (Kyoto Univ.)

Causal/Noncausal Linear Periodically Time-Varying Scaling for Robust Stability Analysis and Their Properties

Scheduled for presentation during the Regular Session "Sampled-data control I" (TuA09), Tuesday, July 25, 2006, 11:40−12:05, Room J

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on June 23, 2024

Keywords Sampled-data control, Periodic systems, Operator methods

Abstract

Stimulated by a general necessary and sufficient condition for robust stability of sampled-data systems derived through the Nyquist stability criterion in an operator-theoretic framework, linear periodically time-varying (LPTV) scaling to sampled-data systems was introduced in a recent study. This paper extends that study, first by generalizing the underlying robust stability theorem in such a way that noncausal LPTV scaling is allowed. It is then demonstrated that noncausal LPTV scaling is quite effective for further reducing conservativeness in the promising approach with LPTV scaling. It is also shown that (even static) noncausal LPTV scaling induces a type of frequency-dependent scaling that is quite different from and, in the context of sampled-data systems and continuous-time periodic systems, more natural than the conventional LTI frequency-dependent scaling. Second, we establish on the other hand that, in the context of continuous-time LTI system analysis, causal/noncausal LPTV scaling offers no advantage over the conventional LTI scaling in a qualitative sense, no matter what class and structure of the uncertainty set and/or scaling are considered. At the same time, however, a remark is given as to a possibility that noncausal LPTV scaling could be useful in some practical sense even in the continuous-time LTI setting, despite its non-superiority mentioned above.