Linear periodically time-varying scaling and its properties

Linear periodically time-varying scaling and its properties

Stimulated by a general necessary and sufficient condition for robust stability of sampled-data systems stated in an operator-theoretic framework, we introduce a novel technique called linear periodically timevarying (LPTV) scaling. We then give a simple example of sampled-data systems in which this new scaling allows exact robust stability analysis for static uncertainties while the convention...

Noncausal linear periodically time-varying scaling for discrete-time systems

A novel technique called noncausal linear periodically time-varying (LPTV) scaling was introduced recently, and it was shown that even static noncausal LPTV scaling has an ability of inducing frequency-dependent scaling if it is interpreted in the context of the conventional scaling approach. Motivated by this preceding study of ours, this paper studies to exploit this attractive property and d...

Discrete-Time Noncausal Linear Periodically Time-Varying Scaling for Robustness Analysis and Controller Synthesis

Since modeling of real plants inevitably gives rise to modeling errors regarded as uncertainties, considering robustness for the uncertainties is important in actual control problems. For tackling issues of analyzing robust stability of closed-loop systems in a less conservative fashion, the μ-analysis method is known to be effective. As an alternative approach to robust stability analysis, on ...

Properties of discrete-time noncausal linear periodically time-varying scaling and their relationship with shift-invariance in lifting-timing

Realization and identification of autonomous linear periodically time-varying systems

Subsampling of a linear periodically time-varying system results in a collection of linear time-invariant systems with common poles. This key fact, known as “lifting”, is used in a two step realization method. The first step is the realization of the time-invariant dynamics (the lifted system). Computationally, this step is a rank-revealing factorization of a block-Hankel matrix. The second ste...