SUMMARY

The thesis analyzes the input to state stability properties of control Lyapunov functions which stabilize nonlinear hybrid systems. Systems that are input to state stable tend to be robust to modeling and sensing uncertainties. It will be shown that given the class of stabilizing control Lyapunov functions, there exists a subset of this class of control Lyapunov functions that input to state stabilize the given hybrid system; called the input to state stabilizing control Lyapunov functions. Bipedal robots, which can be naturally modeled as a hybrid system, is analyzed theoretically and experimentally under this class of controllers. Controllers like asymptotically stabilizing control Lyapunov functions, exponentially stabilizing control Lyapunov functions and rapidly exponentially stabilizing control Lyapunov functions will be considered. With these controllers, the input to state stability analysis will be mainly conducted on two kinds of input uncertainties: parameter and phase, which are frequently observed in bipedal robots. The end result is the construction of input to state stabilizing controllers that are indeed robust to these two uncertainties.