Robust stability analysis of sampled-data systems with noncausal periodically time-varying scaling: Optimization of scaling via approximate discretization and error bound analysis

A novel idea called noncausal linear periodically time-varying (LPTV) scaling has been proposed for robust stability analysis of sampled-data systems. This paper gives a method for approximately optimizing noncausal LPTV scaling by establishing a link between the noncausal LPTV scaling of sampled-data systems and the conventional scaling of discrete- time systems. More precisely, applying what we call the fast- lifting technique, we derive a discrete-time system that is approximately equivalent to the sampled-data system with respect to the optimization of scaling parameters. We further give a method for computing an upper bound of the associated approximation error, together with a few methods for obtaining reduced error bounds. We then demonstrate the effectiveness of noncausal LPTV scaling through numerical examples.