Stabilization of Distributed Parameter Systems With Delays in the Boundary Based on Predictors

• Published in: IEEE transactions on automatic control Vol. 66; no. 7; pp. 3317 - 3324
• Main Authors: Liu, Dongyi, Wang, Qingcong, Xu, Genqi
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-07-2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adjoint systems; Aerospace electronics; Control systems design; Control theory; Delay effects; Delays; Design parameters; Dimensional stability; Distributed parameter systems; exponential stability; Feasibility; Feedback control; Hilbert space; Mathematical model; Schrodinger equation; state feedback; time delay
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3035586

This article is concerned with the controller design for distributed parameter systems with time delays in the boundary. An implementable control law is presented in light of a state predictor, and a feasible calculation scheme of this control law is provided based on the adjoint theory. The resulting closed-loop system is proved to be exponentially stable. As an application, a one-dimensional Schrödinger equation with a delay input is introduced and the numerical simulation verifies the feasibility of the suggested control law.