Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)
Skip to main content
Open Access Publications from the University of California

Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)

  • Author(s): Chai, J
  • Sanfelice, RG
  • et al.

In this paper, tools to study forward invariance properties with robustness to dis- turbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of dif- ferential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without dis- turbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout the paper to illustrate the main ideas.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View