Delayed feedback implementation of decentralized derivative-dependent control of large-scale systems with input delays and disturbed measurements

• Published in: European journal of control Vol. 79; p. 101079
• Main Authors: Zhang, Jin, Zhang, Hui, Fridman, Emilia
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2024
• Subjects: Decentralized control; Delay-induced stability; Input delay; Large-scale systems; Measurement disturbances; Input delay; Large-scale systems; Delay-induced stability; Decentralized control; Measurement disturbances
• ISSN: 0947-3580
• DOI: 10.1016/j.ejcon.2024.101079

We study decentralized derivative-dependent control of large-scale nth-order systems with input delays via delayed feedback implementation. The unavailable derivatives can be approximated by finite differences giving rise to a time-delayed feedback. In the centralized case, an efficient simple linear matrix inequalities (LMIs)-based method for designing of such static output-feedback and its sampled-data implementation was recently suggested. In the present paper, we extend this design to large-scale systems in the presence of input delays and disturbed measurements. Under the assumption of the stabilizability of the system with small enough input delays and small enough interactions by a state-feedback that depends on the output and its derivatives, a delayed static output-feedback that stabilizes the system is presented by using the current and past disturbed measurements. To compensate the errors due to the input delays, we add the appropriate terms to the corresponding Lyapunov–Krasovskii functional that lead to LMIs conditions. The efficient bounds on the delays preserving that the resulting system is input-to-state stable (ISS) are found by verifying the LMIs. In addition, we employ the vector Lyapunov functional method that may allow larger couplings compared with the existing method. Finally, the effectiveness of the proposed methods is illustrated by numerical examples. •Compared with the existing methods on derivative-dependent control, we consider the large-scale system, for the first time, in the presence of input delays and disturbed measurements.•We employ the vector Lyapunov functional method to obtain a Metzler matrix which may allow larger couplings.•We suggest the sampled-data implementation (that is an application in the practical system) subject to the input delay, which is not trivial.