H ∞ Fuzzy Control for Nonlinear Fourth-Order Parabolic Equation Subject to Input Delay

Abstract

This article discusses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> fuzzy control for the nonlinear fourth-order parabolic equation with input delay via collocated actuator/sensor pairs. We suggest that the interval [0, 1] is divided into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> subdomains, where sensors provide spatially averaged/point discrete-time state measurements. The control design strategy is proposed based on output measurements. We derive constructive conditions ensuring that the resulting closed-loop system is internally exponentially stable and has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance by means of the Lyapunov approach.