Delay-dependent decentralized control for nonlinear similar interconnected large-scale systems
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ORIGINAL ARTICLE
Delay-dependent decentralized control for nonlinear similar interconnected large-scale systems Yuechao Ma1 • Le Zhao1 • Deyou Liu1
Received: 22 April 2015 / Accepted: 24 October 2015 Ó Springer-Verlag Berlin Heidelberg 2015
Abstract In this paper, the problem of delay-dependent decentralized control for a class of nonlinear large-scale interconnected systems with similar structure is investigated, where the linear state vectors, the nonlinear state vectors and the nonlinear interconnections involve time delays. The new similar structure is presented via memory feedback. Based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, a decentralized memory derivative feedback control strategy is proposed to stabilize the resulting interconnected systems uniformly asymptotically, in addition, the stability domain is estimated. Finally, simulation results show the effectiveness of the proposed approach. Keywords Decentralized control Time-delay Similar structure Interconnected systems
1 Introduction On the last decades, the increasing complexity and the large scale of interconnected systems have presented a great challenge to scholars, such as economic systems, aerospace systems and urban traffic networks, etc. [1, 2]. In the research of the control problems for large-scale interconnected systems, many researchers have paid a great deal of attention to design the decentralized controller, which refers to the regulation of complex systems by multiple & Le Zhao [email protected] 1
College of Science, Yanshan University, Qinhuangdao 066004, Hebei, People’s Republic of China
controllers that make decisions based on different sensor information, then for the practicability, dependability and economy, decentralized control has been regarded as a reliable and practicable method [3–6]. In the research front line, interconnected systems with similar structure, for their special structures, have been extensively studied and widely applied in many practical systems. The important results about them can be grossly divided into two groups: the establishment of similar structures and the control problems for similar interconnected systems. On one hand, various similar structures were presented in [7–11]. In Yang [7], the symmetric similar structure was proposed and the structural properties of large-scale systems possessing similar structures were researched; another similar structure was given in Yan [8] by state feedback and then was applied to design the robust controllers with similar structure for uncertain composite large-scale systems possessing similarity; Yan [9] presented a similar structure via static output feedback, based on that, the reduce-order control for a class of nonlinear interconnected systems with mismatched uncertainty was considered; Ma [10] proposed a similar structure via output feedback, further designed the state observer for a class of descriptor large-scale composite systems; Shi [11
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