Moment exponential input‐to‐state stability of non‐linear switched stochastic systems with Lévy noise

Abstract

The moment exponential input-to-state stability (ISS) problem for a class of non-linear switched stochastic systems is studied. A continuously differentiable Lyapunov function with indefinite derivative is introduced, which generalises classic Lyapunov function method. Two situations are considered: (i) synchronous switching, i.e. candidate controllers coincide with system modes; (ii) asynchronous switching, i.e. the candidate controllers have a lag to the switching of the system modes. By employing indefinite derivative Lyapunov function method and average dwell-time approach, sufficient conditions for moment exponential ISS of the systems are derived. Finally, an example is given to illustrate the effectiveness of the authors' results.