Sliding Mode Controllers Design based on Control Lyapunov functions for uncertain LTI systems

Abstract

In this paper, a design method of sliding controllers based on control Lyapunov functions for uncertain LTI systems is proposed. Systems with matched non-vanishing disturbances, unmatched uncertainties and uncertain control coefficient matrix are considered. It is shown that whenever a robust nonlinear controller exists that renders the system quadratically stabilizable, in the absence of matched non vanishing disturbances, there is also an appropriate First-Order Sliding-Mode controller stabilizing the origin, that also renders the equilibrium point robustly stable in presence of perturbations. This shows that Sliding-Mode controllers are not more restrictive than other controllers, at least for the class of uncertain systems considered. Moreover, the design based on control Lyapunov functions provides a natural sliding surface, having an asymptotically stable sliding dynamics, so that with the corresponding sliding mode controller ensures global asymptotic stability of the uncertain system. The efficiency of the proposed SMC control is validated experimentally on a Furuta pendulum benchmark.