Exponential input-to-state stability of delay Korteweg–de Vries–Burgers equations

Abstract

The exponential input-to-state stability (EISS) is studied for delay Korteweg–de Vries–Burgers (DKdVB) equations. DKdVB equations are considered with distributed input and boundary input. Making use of the Lyapunov–Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. Besides the impact of the time delay on the EISS, this sufficient condition also shows the effect of the diffusion term on the EISS. In case of uncertainties of system’s coefficients, robust EISS of uncertain DKdVB equations is investigated. A criterion is obtained to guarantee the EISS for the uncertain DKdVB equation. Two numerical simulation examples are given to illustrate the validity of the derived results.