L₂-gain analysis of reset control for piecewise-affine systems with input saturation

Abstract

This paper is concerned with reset control and ${\mathcal{L}}_2$-gain stability of piecewise-affine systems with input saturation and external disturbance under the framework of hybrid systems. Firstly, we present a reset controller and establish exponential stability conditions of piecewise-affine systems with input saturation under the reset controller. Secondly, sufficient conditions for ${\mathcal{L}}_2$-gain stability of the closed-loop systems with input saturation and external disturbance are provided and a reset controller is designed to enhance the ${\mathcal{L}}_2$-gain performance of piecewise-affine systems with input saturation. Furthermore, robustness to inflations of the flow and jump sets is established. Finally, a numerical simulation is provided to illustrate the results.

Keywords:

• Reset control
• ${\mathcal{L}}_2$-gain stability
• piecewise-affine system
• input saturation
• hybrid system

Disclosure statement

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

Additional information

Funding

This work was supported by Natural Science Foundation of Jiangsu Province [grant number BK20201340] and 333 High-level Talents Training Project of Jiangsu Province.