Towards a Geometric Theory of Hybrid Systems

Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrid manifold (or hybrifold) with the associated hybrid ow on it. This enables us to study hybrid systems as (generally non-smooth)dynamicalsystems from a global geometric perspective. We introduce the notion of topological conjugacy of hybrid systems and locally classify Zeno states in dimension two. We show that the Zeno phenomenon is due to nonsmoothness of the hybrid ow and propose several ways of detecting and removing it. A Lyapunov stability result, capturing examples such as unstable + unstable = stable, concludes the paper.

• Type: Conference
• Year: 2000
• Where: HYBRID
• Authors: Slobodan N. Simic, Karl Henrik Johansson, Shankar Sastry, John Lygeros
• Keywords: Associated Hybrid Ow, Control Systems, HYBRID 2000, Hybrid Systems, Non-blocking Hybrid System