Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

• Published in: IEEE transactions on automatic control Vol. 59; no. 9; pp. 2385 - 2399
• Main Authors: Bresch-Pietri, Delphine, Chauvin, Jonathan, Petit, Nicolas
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Actuators; Asymptotic properties; Automatic; Backstepping; Control systems; Control theory; Delay; Delays; Engineering Sciences; Equations; Feedback; Fuels; Linear systems; Mathematical models; Robustness; Stability analysis; Stabilization; Backstepping; partial differential equation; time-delay systems; prediction-based feedback; delay differential equation; Time-delay systems; Prediction-based feedback; Delay differential equation; Partial differential equation
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2014.2322238

In this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral model. This situation is representative of systems where transport phenomena take place, as is frequent in the process industry. The sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems.