# Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems

# Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems

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.

*Keywords:*
finite-time stability, impulsive dynamical system, vector Lyapunov function, hybrid vector comparison system, hybrid finite-time stabilizing controller, decentralized finite-time stabilizer

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