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

Abstract

The passivity‐based boundary control is considered for stochastic Korteweg–de Vries–Burgers (SKdVB) equations. Both the stochastic input strictly passive (SISP) and stochastic output strictly passive (SOSP) are studied. By introducing Lyapunov functionals and Wirtinger's inequality, sufficient criteria are derived to establish SISP and SOSP for SKdVB equations with boundary disturbances. Moreover, when parameter uncertainties arise in SKdVB equations, the robust stochastic passivity is also investigated and sufficient criteria are presented to achieve the robust SISP and SOSP. Two numerical simulations are employed to show the effectiveness and advantages of our theoretical results.