Fuzzy $\\mathcal {H}_{\\infty }$ Output Feedback Control for Nonlinear NCSs With Quantization and Stochastic Communication Protocol

Abstract

This article investigates the problem of <inline-formula><tex-math notation= LaTeX >$\\mathcal {H}_{\\infty }$</tex-math></inline-formula> dynamic output feedback control for a class of discrete-time nonlinear systems with quantization and stochastic communication protocol (SCP) via Takagi–Sugeno rules. A fuzzy Markov jump model is used to describe the output feedback controller with the measurement output signal quantized by the dynamic quantization strategy and the SCP scheduling behavior for the quantized signal transferring to the controller described via a Markov chain. The purpose of the addressed problem is to design a dynamic output feedback controller such that stability and <inline-formula><tex-math notation= LaTeX >$\\mathcal {H}_{\\infty }$</tex-math></inline-formula> performance for the closed-loop system are guaranteed. For this purpose, the corresponding design conditions for the output feedback controller and the dynamic quantization parameters are presented in terms of solutions to a set of linear matrix inequalities. Finally, two simulation examples are given to prove the effectiveness of the proposed design method.