Sliding mode control of interval type-2 T-S fuzzy systems with redundant channels

This paper investigates the sliding mode control (SMC) of interval type-2 (IT2) T-S fuzzy systems. The measurement outputs are propagated via redundant channels for reducing the probability of packet loss and improving the reliability of data transmission. A key feature for the above problem is that the premise variables and the measurement signals may not be available by the controller, which brings difficulty to stabilize the nonlinear systems. Accordingly, a crucial issue is how to synthesize an implementable SMC law under the redundant channels. To this end, the characteristic of the redundant channels is firstly analyzed and the model of available measurement output signals is established. By employing these available measurements as the premise variables and utilizing the upper and lower bounds of the system membership functions (MFs), new MFs are constructed and the sliding mode controller is synthesized. By introducing some null terms carrying the information of MFs, sufficient conditions are derived in terms of nonlinear matrix inequalities to ensure the stochastically ultimate boundedness of the closed-loop system and the reachability of the specified sliding surface. Besides, a binary genetic algorithm (GA) is introduced to solve the nonlinear criteria via the objective function reflecting the control performance. Finally, a numerical example illustrates the effectiveness of the proposed methods.