Robust synchronization of heterogeneous networks of nonlinear time-varying dynamical systems using set-valued linear complementarity couplings
Résumé
This work is largely concerned with the synchronization of nonlinear time-varying agents, using static couplings designed as linear complementarity constraints (hence possibly set-valued operators). The closed-loop system takes the form of linear complementarity systems with a specific structure. Closed-loop well-posedness, equilibrium points, exponential and finite-time stability, and robustness with respect to uncertainties are carefully studied. Linear complementarity problems and variational inequalities are the main analysis tools. Passivity and maximal monotonicity of operators arguments are used. The time-discretization and practical implementation are studied in detail. Several examples with simulations illustrate the theoretical findings. It is shown that the proposed framework allows to consider new nonsmooth feedback controllers.
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