An invariance principle for nonlinear hybrid and impulsive dynamical systems
- 1 January 2000
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 16 (07431619) , 3116-3122 vol.5
- https://doi.org/10.1109/acc.2000.879139
Abstract
In this paper we develop an invariance principle for dynamical systems possessing left-continuous flows. 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 literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.Keywords
This publication has 19 references indexed in Scilit:
- Generalized Lyapunov and invariant set theorems for nonlinear dynamical systemsSystems & Control Letters, 1999
- Impulsive Differential EquationsWorld Scientific Series on Nonlinear Science Series A, 1995
- Impulsive Differential EquationsSeries on Advances in Mathematics for Applied Sciences, 1995
- Stability results for impulsive differential systems with applications to population growth modelsDynamics and Stability of Systems, 1994
- On quasi stability for impulsive differential systemsNonlinear Analysis, 1989
- Theory of Impulsive Differential EquationsPublished by World Scientific Pub Co Pte Ltd ,1989
- Stability of sets for impulsive systemsInternational Journal of Theoretical Physics, 1989
- Impulsive differential systems and the pulse phenomenaJournal of Mathematical Analysis and Applications, 1989
- Differential Equations with Discontinuous Righthand SidesPublished by Springer Nature ,1988
- Stability with respect to part of the variables in systems with impulse effectJournal of Mathematical Analysis and Applications, 1987