Stability of hybrid dynamic systems : analysis and design.

In this work, the stability of switched linear hybrid dynamic systems is investigated and analyzed. Building on the work of DaCunha [10, 11], a unified and extended version of Lyapunov's Second (Direct) Method is developed for application to hybrid linear systems evolving on arbitrary time scale domains, including a time scale dynamic Lyapunov equation which unifies existing analogues in the discrete and continuous cases. We then develop and implement a generalized common Lyapunov function approach for the stability analysis of switched systems evolving on dynamic domains. This leads to the formulation of two very different but closely related problems in analysis and design. The latter has natural applications to the areas of bandwidth optimization, adaptive control, and μ-dynamics for hybrid systems evolving on time scales. We conclude by applying this new theory to a problem in adaptive control.