Nonsmooth Systems


This research area includes the development of new hybrid systems tools to analyze the stability and robustness of systems described by a complex combination of continuous and discrete subsystems. Efforts focus on the development of mathematical models with different granularity and detail that are amenable for systematic analysis and design. A flexible hybrid systems framework is investigated for analysis and design that allows each agent, the algorithms, and the networks to have hybrid dynamics. Specific efforts target the development of tools for analysis and design to certify properties such as safety, convergence, and robustness for such interconnections of hybrid systems. To develop certificates for such properties, asymptotic stability, input-to-state stability, and invariance for hybrid systems are investigated using strict and non-strict Lyapunov functions as well as barrier functions, including the effects of switching, even between stable and unstable subsystems. Developed tools are systematic and allow true nonlinear dynamics, going beyond traditional linear approaches.


Nonsmooth Systems Project Publications