Global stabilization of linear systems subject to input saturation and time delays

• Published in: Journal of the Franklin Institute Vol. 358; no. 1; pp. 633 - 649
• Main Authors: Wu, Jiawei, Huang, Ling
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.01.2021; Elsevier Science Ltd
• Subjects: Canonical forms; Control systems design; Controllers; Decoupling method; Dynamical systems; Feedback control; Linear programming; Linear systems; Multiagent systems; Numerical analysis; Saturation; Stabilization; State vectors; Systems stability
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.10.040

This note is concerned with global stabilization of linear systems subject to input saturation and time delays. Based on the Luenberger canonical form, two new decoupling methods are proposed. For the decoupled system, according to some special canonical forms, we propose two control laws for systems with input time-delays and systems with input saturation and time-delays, and give explicit conditions to ensure the global stability of the closed-loop system. Two special canonical forms contain time delays in input and state vectors, which is essential in recursive design. In addition, for the system subject to input saturation and time-delay, we introduce some free parameters when designing the controller, which can improve the instantaneous performance of the closed-loop system. Finally, the proposed approach is applied on the multi-agent system to design global stabilizing controllers and the effectiveness of the proposed controllers are illustrated by numerical simulations.