Observer‐based H_∞ control of a stochastic Korteweg–de Vries–Burgers equation

Abstract

This article mainly deals with observer-based H ∞ control problem for a stochastic Korteweg-de Vries-Burgers equation under point or averaged measurements. Due to the nonlinearity of the stochastic partial differential equations, special emphases are given to computation complexity. By constructing an appropriate Lyapunov functional, we derive sufficient conditions in terms of linear matrix inequalities to guarantee the internal exponential stability and H ∞ performance of the perturbed closed-loop system by means of the Lyapunov approach. Consistent simulation results that support the proposed theoretical statements are provided. Finally, we have made important instructions for future research directions.

Dynamic event–triggered security control for stochastic partial differential equation systems via a unified pointwise measurement/control strategy

“…The system is meant to be mean-square exponentially stable if there exist p > 0 and λ > 0 that satisfy the following inequality 40…”

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

“…When stochastic noise enters KdVB equations, it is meaningful to study the stochastic KdVB (SKdVB) equation. In Kang et al [12], observer‐based $$$ H\infty $$$ control has been considered for a SKdVB equation under point or averaged measurements. Our recent work [13] has considered boundary control for a SKdVB equation.…”