Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Abstract

The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.

MIMO Super-Twisting Controller using a passivity-based design

“…T HE super-twisting algorithm is a classic result of Sliding-Mode Control [1], [2], used for control [3] and differentiaton [4]. Its design has been performed by geometric methods [3], using Lyapunov functions [5]- [7] and also frequency domain methods [8]. It is a popular control algorithm because of its unique features and advantages for systems of relative degree 1: it can compensate matched Lipschitz perturbations and uncertainties; it forces the output and its derivative to zero in finite-time, while only requiring knowledge of the output; and it generates a continuous control signal [1], [2].…”