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

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.