An invariance principle for nonlinear hybrid and impulsive dynamical systems

  • Authors:

  • VijaySekhar Chellaboina;Sanjay P. Bhat;Wassim M. Haddad

  • Affiliations:

  • Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO;Department of Aerospace Engineering, Indian Institute of Technology, Mumbai 400 076, India;School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA

  • Venue:
  • Nonlinear Analysis: Theory, Methods & Applications
  • Year:
  • 2003

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Abstract

In this paper we develop an invariance principle for dynamical systems possessing left-continuous flows. Specifically, we show that left-continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.