Luenberger-Like Observers for Nonlinear Time-Delay Systems with Application to the Artificial Pancreas: The Attainment of Good Performance

The analysis and control of time-delay systems has gained increasing interest in the last decades due to the effectiveness of delay differential equations (DDEs) in modeling a wide range of physical and engineering frameworks, such as ecological systems, industrial processes, telerobotic systems, earth-controlled satellite devices, and biomedical engineering. Another significant application area that has recently gained widespread attention is networked and distributed control, which may naturally induce nonnegligible and possibly time-varying delays in the input/output channels. As in the case of systems described by ordinary differential equations (ODEs), a crucial point in most advanced control approaches, such as optimal and robust control, is the possibility to solve the observer problem, that is the design of algorithms that provide full information on the state of the system by real-time processing of few measurements. The reader can refer to the recent edited book on nonlinear delay systems [1] and references therein.