Bounded Backstepping Control and Robustness Analysis for Time-Varying Systems under Converging- Input-Converging-State Conditions *

Frédéric Mazenc 1, 2 Michael Malisoff 3 Laurent Burlion 4 Jerome Weston 3
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : We provide new bounded backstepping results that ensure global asymptotic stability for a large class of partially linear systems with an arbitrarily large number of integrators. We use a dynamic extension that contains one artificial delay, and a converging-input-converging-state assumption. When the nonlinear subsystem is control affine, we provide sufficient conditions for our converging-input-converging-state assumption to hold. We also show input-to-state stability with respect to a large class of model uncertainties, and robustness to delays in the measurements of the state of the nonlinear subsystem. We illustrate our result in a first example that has a nondifferentiable vector field and so is beyond the scope of classical backstepping, and then in a nonlinear example that illustrates how one can combine Lyapunov and trajectory based methods to check our assumptions.
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Frédéric Mazenc, Michael Malisoff, Laurent Burlion, Jerome Weston. Bounded Backstepping Control and Robustness Analysis for Time-Varying Systems under Converging- Input-Converging-State Conditions *. European Journal of Control, Lavoisier, 2018, 42, pp.15-24. ⟨10.1016/j.ejcon.2018.02.005⟩. ⟨hal-01848927⟩

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