Paper TuA09.4
Hagiwara, Tomomichi (Kyoto Univ.)
Causal/Noncausal Linear Periodically TimeVarying Scaling for Robust Stability Analysis and Their Properties
Scheduled for presentation during the Regular Session "Sampleddata control I" (TuA09), Tuesday, July 25, 2006,
11:40−12:05, Room J
17th International Symposium on Mathematical Theory of Networks and Systems, July 2428, 2006, Kyoto, Japan
This information is tentative and subject to change. Compiled on May 27, 2023


Keywords Sampleddata control, Periodic systems, Operator methods
Abstract
Stimulated by a general necessary and sufficient condition for robust stability of sampleddata systems derived through the Nyquist stability criterion in an operatortheoretic framework, linear periodically timevarying (LPTV) scaling to sampleddata 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 frequencydependent scaling that is quite different from and, in the context of sampleddata systems and continuoustime periodic systems, more natural than the conventional LTI frequencydependent scaling. Second, we establish on the other hand that, in the context of continuoustime 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 continuoustime LTI setting, despite its nonsuperiority mentioned above.

