Seminar: Graphical Analysis of Multivariable Systems: Emerging Tools and Applications
Abstract: Graphical representations of univariate systems, such as Nyquist and Bode diagrams, are taught in almost all control curricula and are widely used across engineering domains. These tools are intuitive and informative, enabling many closed-loop properties, including stability and robustness, to be inferred by inspection, and visually assisting with controller design. However, for multivariable systems, the coupling of multi-dimensional information poses challenges as well as opens up many possibilities for extending such graphical tools. In this talk, we examine several emerging tools developed in this direction, including the scaled relative graph (first used by the optimization community) and the Davis–Wielandt shell (first used by the control community), along with their associated feedback stability certificates. In particular, we highlight the connections among these tools and their applications in robust stability analysis. We also outline the key ideas behind their visualization and the validation of their resulting stability conditions.
Bio: Ding Zhang is a Research Fellow in the School of Engineering, The Australian National University. He received the B.Eng. degree in Mechanical Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2018, and the Ph.D. degree in Electronic and Computer Engineering from The Hong Kong University of Science and Technology, Hong Kong SAR, in 2024, where he also worked as a Postdoctoral Research Fellow. He was a visiting student with the EMAN Group at King Abdullah University of Science and Technology, Thuwal, Saudi Arabia, in 2019, and with the Control Group at the University of Cambridge, Cambridge, United Kingdom, in 2023. His research focuses on graphical stability analysis of uncertain and large-scale networked systems, with broader interests in matrix theory, spectral graph theory, and control theory.
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- The Australian National University
- Canberra, Australian Capital Territory
- Australia 2601
- Building: Birch 2.02