Terushkin, Maria; Fridman, Emilia Sampled-data observers for semilinear damped wave equations under spatially sampled state measurements. (English) Zbl 1429.93220 Automatica 106, 150-160 (2019). Summary: Sampled-data observers/controllers under the sampled in space and time measurements were suggested in the past for parabolic systems. In the present paper, for the first time, a sampled-data observer is constructed for a hyperbolic system governed by 1D semilinear wave equation with either viscous or boundary damping. The measurements are sampled in space and time. Sufficient conditions for the exponential stability of the estimation error are derived by using the time-delay approach to sampled-data control and appropriate Lyapunov-Krasovskii functionals. The dual sampled-data controller problems are formulated. Numerical examples including observer design for unstable damped sine-Gordon equation illustrate the efficiency of the method. Cited in 9 Documents MSC: 93C57 Sampled-data control/observation systems 93C20 Control/observation systems governed by partial differential equations 93D20 Asymptotic stability in control theory 35L05 Wave equation Keywords:sampled-data observers; hyperbolic systems; linear matrix inequalities PDFBibTeX XMLCite \textit{M. Terushkin} and \textit{E. Fridman}, Automatica 106, 150--160 (2019; Zbl 1429.93220) Full Text: DOI References: [1] Antsaklis, P.; Baillieul, J., Special issue on technology of networked control systems, Proceedings of the IEEE, 95, 1, 5-8 (2007) [2] Åström, K. 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