Sampled-data observers for delay systems and hyperbolic PDE–ODE loops

Abstract

This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be applied to time delay systems of strict-feedback structure, transport Partial Differential Equations (PDEs) with nonlocal terms, and feedback interconnections of Ordinary Differential Equations with a transport PDE. The proposed design approach consists in exploiting any existing observer that features robust exponential convergence of the error when continuous-time output measurements are available. The (continuous-time) observer is then modified, mainly by adding an inter-sample output predictor, to compensate for the effect of data-sampling. Using small-gain analysis, we show that robust exponential stability of the error is preserved, provided the sampling period is not too large. The results are applied to a chemical reactor and to the class of triangular globally Lipschitz delay systems.