A diffusive representation approach toward H_∞ sliding mode control design for fractional-order Markovian jump systems

摘要

This article proposes a new H-infinity sliding mode control strategy for stabilizing controller design for fractional-order Markovian jump systems. The suggested approach is based on the diffusive representation of fractional-order Markovian jump systems which transforms the fractional-order system into an integer-order one. Using a new Lyapunov-Krasovskii functional, the problem of H-infinity sliding mode control of uncertain fractional-order Markovian jump systems with exogenous noise is investigated. We propose a sliding surface and prove its reachability. Moreover, the linear matrix inequality conditions for stochastic stability of the resultant sliding motion with a given H-infinity disturbance attenuation level are derived. Eventually, the theoretical results are verified through a simulation example.