Exponential Stabilization of Polynomial Fuzzy Positive Switched Systems With Time Delay Considering MDADT Switching Signal

Nonlinear switched positive systems with a time delay are universally found in practical applications. However, with the consideration of the switching signal, the constraints of positivity and the existence of the time delay make the control of this special system much more complicated. In this article, a novel exponential stability analysis that can tighten the bounds of switching dwell time is proposed under the switched positive polynomial fuzzy control scheme. First, the polynomial fuzzy model represents the dynamic characteristics of nonlinear switched positive systems with a time delay, which can sufficiently promote the approximation capability, thereby simplifying the model structure. Second, the switched polynomial state fuzzy controller is designed based on the principle of the premise variable mismatching to enhance the design flexibility, and matrix decomposition is proposed to overcome the obstacle caused by the nonconvexity conditions both in positive and stable conditions. In addition, as the existing switching control theory is relatively conservative, which leads to a high bound of dwell time, a switched fuzzy copositive Lyapunov–Krasovskii function with the upper bound of the derivative of the membership function and a Taylor expansion technique are together incorporated in a positive switched stability analysis to obtain tight bound of dwell time and relax conditions. At last, two simulation examples are provided to validate the proposed methods.