Synchronization of Liénard-type oscillators in heterogenous electrical networks

Motivated by potential applications for power-electronic converters in microgrids, we study the problem of global asymptotic synchronization of Liénard-type nonlinear oscillators in heterogenous LTI electrical networks with series R-L circuits modeling interconnections. By heterogeneous, we mean that the resistance-to-inductance ratios of the lines are not all the same. Building on our previous work, we derive sufficient conditions for global asymptotic synchronization by using a first-order filter on the outputs of the oscillators. Our approach leverages a coordinate transformation to a system that emphasizes signal differences and the use of passivity based arguments to establish synchronization of the network of oscillators asymptotically. The analysis subsumes and generalizes previous conditions that have been derived for Liénard oscillators in homogeneous electrical networks. Numerical simulations are provided to validate the results.