Estimation of Domain of Attraction for Discrete-Time Positive Interval Type-2 Polynomial Fuzzy Systems With Input Saturation

This article focuses on expanding the estimation of the domain of attraction (DOA) for discrete-time positive nonlinear systems subject to input saturation and parameter uncertainties. To facilitate analysis and design, the interval type-2 (IT2) polynomial fuzzy model is used to represent the nonlinear plant and capture uncertainties. Combining with the IT2 polynomial fuzzy controller, the discrete-time positive IT2 polynomial fuzzy-model-based (PIT2PFMB) control system is formed to facilitate analysis. To enlarge the estimation of DOA of the discrete-time PIT2PFMB system, polyhedron is used to characterize the DOA with the help of linear copositive Lyapunov function (LCLF). Referring to the nonconvex conditions derived by LCLF, an effective convexification method is proposed in this article. For comparison purposes, the saturation-dependent-Lyapunov-function-based method is extended to the PIT2PFMB control system by adding the corresponding positivity conditions. In addition, this article attempts to enlarge the estimation of the DOA by improving the IT2 membership-function-dependent (IT2MFD) method and extending it to all conditions, including the stability conditions and the DOA estimation conditions. Finally, an example with simulation results is given to verify the effectiveness of all the methods proposed in this article for expanding the estimation of the DOA.