Tracking control of T-S fuzzy systems under probabilistic constraints and fading channels

This work investigates the probabilistic-constrained tracking control problem for T-S fuzzy systems under fading channels described by the memoryless multiplicative noise model. The main control objective is to confine the tracking error into its pre-given bounds no lower than a certain probability. To this end, a tracking controller is firstly synthesised by introducing the fading parameter as an amplification factor towards 'retrieving' the original information to some extent. An auxiliary function and the multi-dimensional Chebyshev inequality make it possible to derive sufficient conditions such that the tracking error falls into its specified domain with a frequency larger than a pre-given value. By employing an inequality involving unmatched membership functions of the controller and fuzzy system, the favourite property of matched membership functions can be employed. A numerical example illustrates the effectiveness of the proposed method.