Refined exponential stability analysis of a coupled system *. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Safi, Mohammed; Baudouin, Lucie; Seuret, Alexandre
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 11972
• Page End: 11977
• Publication Date: 2017-07
• Subjects: Transport equation -- Lyapunov stability -- integral inequalities; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.1758
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: The objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.