Passivity-based boundary control for Korteweg-de Vries-Burgers equations

This article considers the passivity-based boundary control for Korteweg-de Vries-Burgers (KdVB) equations. Both the input strict passivity (ISP) and the output strict passivity (OSP) are studied. By the Lyapunov functional method and Wirtinger's inequality, sufficient criteria are derived to establish ISP and OSP for KdVB equations with boundary disturbances. Moreover, when parameter uncertainties arise in KdVB equations, the robust ISP and OSP are also investigated and sufficient criteria are proposed to achieve the robust ISP and OSP. Simulation examples are also given to verify the effectiveness of theoretical results.