Stabilization Analysis and Impulsive Controller Design for Positive Interval Type-2 Polynomial Fuzzy Systems

Abstract

This article investigates the polynomial fuzzy impulsive control problem for positive nonlinear systems subject to parameter uncertainties. The positive nonlinear systems are represented as positive interval type-2 (IT2) polynomial fuzzy-model-based systems, while the parameter uncertainties are captured by the IT2 membership functions (MFs). Considering that the controller being designed needs to be implementable and practical, in addition to ensuring the positivity and stability of the system, there are still some potential requirements for the controller, such as lower implementation cost and control cost. To reduce the implementation cost, the IT2 polynomial fuzzy impulsive controller is designed under the imperfect premise matching concept that the premise MFs and the number of rules of fuzzy controller are different from those of fuzzy model. To reduce the control cost, the impulsive controller that can tolerate larger impulse control interval (ICI) is designed by the following two novel methods. The first one is the proposed impulse-time-dependent discretized polynomial copositive Lyapunov function whose Lyapunov variable is designed as the interpolation polynomial function of time. The second one is the advanced IT2 membership-function-dependent (IT2MFD) analysis method which is improved by a novel footprint of uncertainty partitioning method proposed by this paper, so that this advanced IT2MFD method can alleviate the negative impact of parameter uncertainties on the ICI. Finally, a simulation example using lipoprotein metabolism and potassium ion transfer model as the nonlinear system to be controlled is used to verify the effectiveness of the proposed impulsive control methods.