This two-part seminar will overview several traditional and novel analysis tools for stability and control of nonlinear dynamical systems. Topics to be covered will include Lyapunov Theory, Passivity and Monotonicity, as well as the differential versions of it. Emphasis will be made on the limitations of each technique and how these limitations affect their application spectrum.
Throughout the talks I will describe the importance of these tools in the study of networked dynamical systems. In particular, I will use a canonical model for synchronization of networked oscillators as a motivating example, and describe how to apply these tools in their study. Along the way, I will highlight a few commonly incurred mistakes and the possible workarounds.