Robust fuzzy control for stochastic Markovian jumping systems via sliding mode method

Abstract

This paper considers the problem of sliding mode control for stochastic Markovian jumping systems by means of fuzzy method. The Takagi–Sugeno (T–S) fuzzy stochastic model subject to state-dependent noise is presented. A key feature in this work is to remove the restricted condition that each local system model had to share the same input channel, which is usually assumed in some existing results. The integral sliding surface is constructed for every mode and the connections among various sliding surfaces are established via a set of coupled matrices. Moreover, the present sliding mode controller including the transition rates of modes can cope with the effect of Markovian switching. It is shown that both the reachability of sliding surfaces and the stability of sliding mode dynamics can be ensured. Finally, numerical simulation results are given.

Keywords:

• Markovian jumping systems
• T–S fuzzy model
• state-dependent noise
• sliding mode control

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by NNSF from China [grant number 61273073].