Abstract:In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an error heat equation with time-delay. Inspired by recent developments in the area of delayed ODEs, we propose novel Lyapunov functionals based on the Legendre polynomials. Then, new Bessel-Legendre (BL) inequalities are provided to derive sufficient stability conditions in the form of linear matrix inequalities (LMIs) that are parameterize… Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.