Restricted partial stability and synchronization

In this paper we combine partial stability and set invariance methods, which is a necessary development for applications such as synchronization. We use set invariance methods to ensure that the 'auxiliary' variables remain on a restricted domain, and then use this framework to develop new results for both local and global partial stability theory. We apply the methodology to identical synchronization of oscillator networks, which gives rigorous conditions for existing local methodology as well as novel global methodology. The work also allows a common framework for synchronization analysis of both oscillator networks and power systems. We show the applicability by finding novel synchronization conditions for an example oscillator network.