Small‐gain based stabilizing control for hybrid systems: Application to bipedal walking robot

Abstract

This study presents a systematic methodology for developing a stabilizing controller for a general hybrid systems model. The approach is based on utilizing the small‐gain theorem as a means of constructing the Lyapunov function and analyzing the input–output stability of the subsystems in the feedback loop. By considering the control system in a closed‐loop configuration with the hybrid system, the small‐gain theorem can be applied. In this scheme, a dynamic control system is proposed that satisfies the closed‐loop stability conditions. This method applies to various hybrid systems' applications due to its generality. To demonstrate the effectiveness and performance of the proposed control approach, two simulation examples, including a linear hybrid system and a bipedal walking robot, are examined.