Abstract
This article investigates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> -exponential stabilization and positivity of the controlled discrete-time polynomial fuzzy model (DPFM) system with time delay. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> -exponential polynomial copositive Lyapunov candidate is proposed to detect the system stability under the convergence (decay) rate. Static output feedback fuzzy controller is then synthesized to assure the DPFM closed-loop system with time delay. We propose Chebyshev membership functions (CMFs) to approach the primary membership function and attenuate the conservativeness of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> -exponential stability formulation and positivity analysis. Chebyshev norm approximation error is utilized to introduce the error between CMFs and primary membership functions using slack matrices. A numerical example is presented to validate the proposed methods.
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