Approximations of Lyapunov functionals for ISS analysis of a class of higher dimensional nonlinear parabolic PDEs. (March 2021)

• Record Type: Journal Article
• Authors: Zheng, Jun; Zhu, Guchuan
• Is Part Of: Automatica. Volume 125(2021)
• Publication Date: 2021-03
• Subjects: Approximation of Lyapunov functionals -- ISS -- iISS -- L1-norm -- Nonlinear parabolic PDEs; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.109414
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper introduces a novel method, namely the approximations of Lyapunov functionals, for input-to-state stability (ISS) analysis of a class of higher dimensional nonlinear parabolic partial differential equations (PDEs) with variable coefficients. Specifically, for any q ∈ [ 1, + ∞ ] and the considered nonlinear parabolic PDEs with different types of boundary disturbances in L l o c q ( R + ; L 1 ( ∂ Ω ) ) and initial data in L 1 ( Ω ), we show that ISS-like estimates in L 1 -norm (or weighted L 1 -norm) can be established by constructing approximations of (coercive and non-coercive) Lyapunov functionals. Some examples are provided to illustrate the application of the proposed method.