Scaled Graph Bounding Techniques for Reset Systems
Provides theoretical insights for control engineers working on graphical analysis of reset systems, but the contribution is incremental.
This paper develops techniques to over-bound the scaled graph of reset systems, revealing a fundamental limitation of quadratic-dissipativity-based approximation methods.
Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset systems, in line with widely adopted loopshaping methods for linear systems. The aim of this paper is to derive techniques for over-bounding the scaled graph of reset systems, and obtain insights in their accuracy. We exploit connections between quadratic dissipativity and scaled graphs to recast the over-bounding problem as the search for piecewise quadratic storage functions. Using specific sampling techniques, we reveal a fundamental limitation of general scaled graph approximation methods that are based on quadratic dissipativity.