Bounded backstepping control and robustness analysis for time-varying systems under converging-input-converging-state conditions
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.
Publication Source (Journal or Book title)
European Journal of Control
Mazenc, F., Malisoff, M., Burlion, L., & Weston, J. (2018). Bounded backstepping control and robustness analysis for time-varying systems under converging-input-converging-state conditions. European Journal of Control, 42, 15-24. https://doi.org/10.1016/j.ejcon.2018.02.005