Stabilization of nonlinear delay systems using approximate predictors and high-gain observers

• Published in: Automatica (Oxford) Vol. 49; no. 12; pp. 3623 - 3631
• Main Authors: Karafyllis, Iasson, Krstic, Miroslav
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.12.2013; Elsevier
• Subjects: Adaptative systems; Applied sciences; Approximation; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Delay; Delay systems; Detection, estimation, filtering, equalization, prediction; Dynamical systems; Exact sciences and technology; Information, signal and communications theory; Modelling and identification; Nonlinear dynamics; Nonlinear systems; Observers; Sampled-data control; Sampling; Signal and communications theory; Signal, noise; Stabilization; Telecommunications and information theory; Sampled-data control; Delay systems; Nonlinear systems; Input output; High gain observer; Sampled system; Stabilization; Non linear control; Feedback regulation; Delay system; Non linear system; Global solution; Digital control; Successive approximation; Linear prediction; Linear system; Sampling theory; Lipschitz function; Robustness; Sampling; Output feedback
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2013.09.006

We provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. The solution is global, employs the predictor approach over the period that combines the input and output delays, addresses nonlinear systems with sampled measurements and with control applied using a zero-order hold, and requires that the sampling/holding periods be sufficiently short, though not necessarily constant. Our approach considers a class of globally Lipschitz strict-feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map, a high-gain sampled-data observer, and a linear stabilizing feedback for the delay-free system. The obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered. The approach is specialized to linear systems, where the predictor is available explicitly.