Finite time stability of singularly impulsive dynamical systems

In this paper we present finite-time stability results for nonlinear singularly impulsive dynamical systems by using quasi-Lyapunov function approach. Motivated by the results on impulsive dynamical systems presented in Haddad, Chellaboina, and Kablar (2001a-b) and Haddad, Kablar, Chellaboina (2000, 2005) and the authors previous work on singular or generalized systems, in Kablar (2003) is presented new class of singularly impulsive or generalized impulsive dynamical systems. This systems presents novel class of hybrid systems and generalization of impulsive dynamical systems to incorporate singular nature of the systems. Extensive applications of this class of systems can be found in contact problems and in hybrid systems. In this paper we develop finite time stability results for this class of systems by using quasi-Lyapunov function approach. To the best knowledge of author results are nonexistent in the literature.