Input to State Stabilizing Control Lyapunov Functions for Hybrid Systems

Abstract

The thesis analyzes the input-to-state stability (ISS) properties of control Lyapunov functions (CLFs) that stabilize hybrid systems. Systems that are input-to-state stable tend to be robust to modeling and sensing uncertainties. This dissertation will show that, given the class of control Lyapunov functions (CLFs), a subset of this class of control Lyapunov functions (CLFs) that input-to-state stabilize the given hybrid system, exists. These functions are called the input-to-state stabilizing control Lyapunov functions (ISS-CLFs). As an application, these ISS-CLFs are constructed for bipedal robots, which belong to a special class of hybrid systems: systems with impulsive effects. Bipedal robotic behaviors such as walking, running and dancing are implemented by utilizing variants of input-to-state stabilizing controllers both in simulations and experiments.