An invariance principle for nonlinear hybrid and impulsive dynamical systems

✍ Scribed by VijaySekhar Chellaboina; Sanjay P. Bhat; Wassim M. Haddad

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 290 KB
• Volume: 53
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00316-4

✦ Synopsis

In this paper we develop an invariance principle for dynamical systems possessing leftcontinuous ows. Speciÿcally, we show that left-continuity of the system trajectories in time for each ÿxed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-inÿnite interval are su cient 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.