Control of Uncertain Systems under Bounded Chattering

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In this paper, we propose a mathematical method to compute a robust control with bounded chattering enabling to stabilize a uncertain dynamical system around an equilibrium of the nominal system (non disturbed system) The idea is to consider the problem in the framework of differential games and to treat the stabilization problem as a state constraint inspired from a Lyapunov characterization. The notion of Leadership kernel then provides states and controls allowing the system to converge exponentially to a neighborhood of the equilibrium.

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