This chapter describes sufficient conditions for finite-time stability of nonlinear impulsive dynamical systems. For impulsive dynamical systems, it may be possible to reset the system states to an equilibrium state, in which case finite-time convergence of the system trajectories can be achieved without the requirement of non-Lipschitzian dynamics. Furthermore, due to system resettings, impulsive dynamical systems may exhibit non-uniqueness of solutions in reverse time even when the continuous-time dynamics are Lipschitz continuous. The chapter presents stability results using vector Lyapunov functions wherein finite-time stability of the impulsive system is guaranteed via finite-time stability of a hybrid vector comparison system. These results are used to develop hybrid finite-time stabilizing controllers for impulsive dynamical systems. Decentralized finite-time stabilizers for large-scale impulsive dynamical systems are also constructed. Finally, it gives a numerical example to illustrate the utility of the proposed framework.
Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Systems