L2 Gain And Passivity Techniques In Nonlinear Control

By Diana Bohm. 2016

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Conditions for stability of droop-controlled inverter-based microgrids (2014, methodology): “…Maschke, & Escobar, 2002; Schiffer, Ortega, Astolfi, Raisch, & Sezi, 2014), we represent the lossless microgrid system in port-Hamiltonian form (van der Schaft, 2000) to identify the energy-Lyapunov function and give conditions for stability of the frequency synchronization equilibrium state.”
Output-Based and Decentralized Dynamic Event-Triggered Control With Guaranteed $\mathcal{L}_{p}$- Gain Performance and Zeno-Freeness (2017, background): “A convenient way to analyze the Lp-gain of a control system is by constructing a so-called storage function S, which is positive semi-definite, and satisfies the dissipation inequality Ṡ θ|w| − |q(x,w)| during flow and S S at jumps, where θ|w| − |q(x,w)| is the supply rate, θ an upper bound for the ”
On Lyapunov functions and data-driven dissipativity (2017, background): “The theory of dissipativity, first introduced in Willems (1972), plays an important role when dealing with control problems (see Van der Schaft (2012); Hill and Moylan (1980); Ghanbari et al. (2016)).”