Robust Tracking Control of Interval Type-2 Positive Takagi–Sugeno Fuzzy Systems With External Disturbance

Nonlinear positive systems are ubiquitous in practical applications. The constraint of positive conditions makes the design of this system still quite challenging even for the existing advanced control theory. In addition, when uncertainty and external disturbance also act on the positive nonlinear system at the same time, it will aggravate the complexity of the problem. In response to this problem, for the first time, this article presents a feasible robust tracking control strategy for the positive nonlinear systems with external disturbance and subject to uncertainty. In the proposed control strategy, the positive Takagi–Sugeno (T–S) fuzzy model is used to effectively represent the nonlinearity of the positive system, and the interval type-2 (IT2) fuzzy sets are used to deal with the uncertainty. The focus of tracking control is to design a reasonable IT2 fuzzy controller, which can make the states of the plant follow those of the given stable positive reference system as accurately as possible under the $H_\infty$ performance. Different from the tracking control research of general systems in the existing literature, in the tracking control analysis of positive systems, the generation of nonconvex conditions is inevitable. This article smoothly removes the obstacle of this problem. In addition, this article successfully attempts to relax the conservativeness of the basic analysis conditions by improving IT2 membership-function-dependent method, thereby improving the tracking effect under $H_\infty$ performance. Finally, a detailed simulation example is given to verify the effectiveness of the proposed strategy.