Stability Analysis of Nonlinear Impulsive Stochastic Systems with Lyapunov Indefinite Derivative

摘要

The properties of input-to-state stability (ISS), integral input-to-state stability (IISS) and stochastic input-to-state stability (SISS) are discussed for impulsive stochastic nonlinear systems with Lyapunov indefinite derivative in this paper. The Lyapunov time derivative is indefinite, it can be positive or negative, which means it can be applied to a wider range than other ordinary Lyapunov function. Through the use of average dwell-time (ADT) method, the ISS, SISS and IISS properties are derived in the paper. By now, there is no literature on such properties of nonlinear impulsive stochastic systems with Lyapunov indefinite derivatives. In the end, an example is presented to illustrate the validity of this outcome.