Time‐varying control for exponential stabilisation of the Brockett integrator

Abstract

This study investigates the time-varying control for globally exponential stabilization of the Brockett integrator. Using the desired trajectory as a virtual control, the authors first illustrate the concept behind the control design and then propose an initial-value-dependent time-varying control. While this time-varying control offers a simple and analytic solution to the problem of exponential stabilisation for the Brockett integrator, it may fail if one of the initial states is zero. To resolve this initial-value-dependent issue, they develop a new time-varying control to globally and exponentially stabilise the Brockett integrator to the origin without using any state or input transformation. They present the stability analysis and numerical results to verify the effectiveness of the proposed time-varying stabilisation control.