Razumikhin-type Control Lyapunov and Barrier Functions for Time-Delay Systems

TL;DR

This paper introduces Razumikhin-type control Lyapunov and barrier functions tailored for nonlinear time-delay systems, enabling simultaneous stabilization and safety control design, extending existing methods to systems with delays.

Contribution

It proposes novel Razumikhin-type control Lyapunov and barrier functions for time-delay systems, integrating stabilization and safety control in a unified framework.

Findings

Successfully extends control Lyapunov and barrier functions to time-delay systems.

Demonstrates the approach with a numerical example.

Provides a new method for simultaneous stabilization and safety in delayed systems.

Abstract

This paper studies the stabilization and safety problems of nonlinear time-delay systems, where time delays exist in system state and affect the controller design. Following the Razumikhin approach, we propose a novel control Lyapunov-Razumikhin function to facilitate the controller design and to achieve the stabilization objective. To ensure the safety objective, we propose a Razumikhin-type control barrier function for time-delay systems for the first time. Furthermore, the proposed Razumikhin-type control Lyapunov and barrier functions are merged such that the stabilization and safety control design can be combined to address the stabilization and safety simultaneously, which further extends the control design from the delay-free case into the time-delay case. Finally, the proposed approach is illustrated via a numerical example.