Robust Stabilisation of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes

This paper addresses the robust stabilisation problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a non-parallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for T-S fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analysed and the sliding mode controller is parameterised in terms of the solutions of a set of linear matrix inequalities (LMIs) which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.