Quantiser-based Hands-off control for robust [𝒦, 𝒦ℒ] sector

Abstract

This article discusses a quantiser-based stabilisation problem for uncertain nonlinear systems with the aid of robust $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{KL}\mathcal{]}$ sector. We confirmed that the quantised-feedback control steers the state trajectories of the uncertain nonlinear systems within the robust $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{KL}\mathcal{]}$ sector in finite time by adjusting the quantisation parameters. Furthermore, control-Lyapunov functions are helpful to obtain sufficient conditions for ensuring the closed-loop system's asymptotic stability and the reachability of the robust $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{KL}\mathcal{]}$ sector. Finally, a nonlinear electronic circuit is provided to test the effectiveness of the designed control law.

Keywords:

• Robust $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{KL}\mathcal{]}$ sector
• signal quantisation
• control-Lyapunov function
• mean-value theorem
• hands-off control

Disclosure statement

No potential conflict of interest was reported by the author(s).