Hybrid-Triggered H∞ Control for Parabolic PDE Systems Under Deception Attacks

Abstract

A hybrid-triggered controller is designed in this article to analyze the stabilization of parabolic type partial differential equations (PDEs) with deception attacks and disturbances. The hybrid-triggered controller is designed by combining time-triggered and event-triggered controllers with the aid of a Bernoulli random variable. A nonlinear function is considered to describe the deception attack signal and the probability of occurrence of deception attack signals will be determined by a Bernoulli random variable. An <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 is utilized to attenuate the occurrence disturbances. We employ a Lyapunov-Krasovskii functional (LKF) to analyze the stabilization of the chosen PDE under the proposed controller and the stabilization conditions are obtained in terms of linear matrix inequalities (LMIs). Numerical examples are given finally to check the efficacy of the derived results.