Output-feedback-guaranteed cost control of fractional-order uncertain linear delayed systems
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Output-feedback-guaranteed cost control of fractional-order uncertain linear delayed systems Liping Chen1 · Tingting Li1 · Ranchao Wu2 · António M. Lopes3 · J. A. Tenreiro Machado4 · Kehan Wu5 Received: 19 November 2019 / Revised: 1 April 2020 / Accepted: 5 July 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract The control of fractional-order (FO) delayed systems is important in real-world applications, but it is still a challenging task. This paper studies the output-feedback-guaranteed cost control of a class of FO uncertain linear systems with time delay. Norm-bounded and time-varying parameter uncertainties are considered. A new definition of guaranteed cost control of FO system is proposed. Additionally, static and dynamic output-feedback delay-independent guaranteed cost controllers are designed. Two numerical examples are presented showing the effectiveness of the proposed schemes. Keywords Fractional-order system · Guaranteed cost control · Output feedback · Time delay Mathematics Subject Classification 93Cxx · 34Hxx · 93Dxx
1 Introduction Fractional calculus generalizes the standard calculus to fractional orders (FO). The FO integral and differential equations can describe the dynamics of complex systems accurately with a reduced number of parameters. Indeed, the FO equations capture the history of the system
Communicated by Luz de Teresa.
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Liping Chen [email protected]
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School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China
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School of Mathematics, Anhui University, Hefei 230601, China
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UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
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Training Center of Anhui Provincial Electric Power Company, Hefei 230000, China 0123456789().: V,-vol
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dynamics and overcome the shortcomings of the classic integer models that do not conform adequately with the experimental results observed in many real phenomena (Hilfer 2000; Luo and Chen 2012; Xue 2017; Monje et al. 2010; Chen et al. 2020). Therefore, fractional calculus has been used in various fields of natural and social sciences, such as in physical mechanics, anomalous diffusion, automatic control, signal processing, biomedicine, and others (Podlubny 1999; Kilbas et al. 2006; Lopes et al. 2016; Machado et al. 2015; Chen et al. 2019, 2017). The robustness and performance analysis of FO systems have attracted the attention of many researchers, with particular focus on the stability of FO uncertain linear systems. In recent years, we find considerable research on the stability and stabilization of general FO systems (Monje et al. 2008; Xu et al. 2020; Zou et al. 2018; Chen et al. 2012, 2015; Ding et al. 2015; Yu and Jiao 2013). For example, (Zhang et al. 2015) discussed the stability of n-dimensional FO nonlin
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