A new framework for stability analysis of networked control systems

Abstract:

A quantized feedback system is a control system in which finite-level quantization of signal values is involved in the feedback loop. Quantized feedback is found in many engineering systems including mechanical systems and networked systems because multilevel-valued devices such as A/D (Analog-to-Digital) converters, on/off switching actuators, and digital communication networks are widely used in these systems. The purpose of this research is to establish a unified approach for the stability analysis of quantized feedback systems. In this talk, we begin our study with discussing the difficulties typically involved in stability analysis of quantized feedback systems. Specifically, by showing that traditional notion of lp stability and the well-known small gain theorem are too strong in the presence of the data rate constraint and cannot be successfully applied to many of quantized feedback systems, we discuss the need for introducing an appropriate local stability notion and a local stability analysis framework based on it. Motivated by the observation, a new notion of small lp signal lp stability is introduced. It is a local stability notion which is defined in terms of local upper bounds on input-output signal norms. We derive a sufficient condition for a feedback system to be small lp signal lp stable. With all new notions and theorems, a new framework for local stability analysis of quantized feedback systems is developed. A new class of uncertainty, level bounded uncertainty, is also introduced in this work. This is useful in approximating some classes of nonlinearities that include quantization errors. Finally, the usefulness of the proposed framework is demonstrated with examples.

Presentation Slides

Biography:Yumiko Ishido received her Bachelor of Engineering, Master of Informatics, and
Doctor of Informatics degrees from Kyoto University, Japan, in 2006,
2008 and 2012, respectively. She is currently working as a
post-doctoral fellow at the Department of Automatic Control, Lund
University, Sweden. Her research interests include control of
networked systems, hybrid systems, and nonlinear systems.