The Stability Analysis for a 2 × 2 Conservation Law with PI Controller and PDP Controller

Abstract

This article is concerned with the stability analysis of a $2\times 2$ conservation law with PI and PDP boundary feedback control. In the PI controller case, the authors establish a sufficient and necessary stability condition for feedback parameters by Walton–Marshall criterion. Moreover, in PDP controller case, the characteristic equation is an exponential polynomial which includes two exponential arguments. Based on Ruan’s results on stability for quasi-polynomials and Schur–Cohn criterion on the roots inside the unit circle for a real coefficient polynomial, a complete characterization for system parameters and the feedback delay is presented. Also, the delay-independent and delay-dependent stability intervals are obtained in this article.