Distributed functional observers for fractional-order time-varying interconnected time-delay systems
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Distributed functional observers for fractional-order time-varying interconnected time-delay systems Dinh Cong Huong1 Received: 8 July 2020 / Revised: 16 September 2020 / Accepted: 5 October 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract Our main purpose in this paper is to design distributed functional observers for a class of fractional-order time-varying interconnected time-delay systems. The contributions of this paper conclude three aspects. First, we propose novel functional observers for subsystems of the fractional-order time-varying interconnected time-delay systems. The designed distributed functional observers in this paper work for a wider class of interconnected time-delay systems in the sense that when some existing design methods cannot be applied to estimate linear functions of the state vector, the distributed functional observers in this paper can still estimate linear functions of the original state vector. Then, we establish existence conditions for the proposed functional observers. Finally, we provide effective algorithms for computing unknown observer matrices. Keywords Fractional-order interconnected systems · Distributed functional observers · Time-varying · Time-delay Mathematics Subject Classification 34H05 · 93B07 · 93B51
1 Introduction Fractional-order systems have been widely applied in many important areas, including electrical circuits (Jesus et al. 2008; Kaczorek 2011; Kaczorek and Rogowski 2015), population dynamics (Ahmed et al. 2007), biotechnology (Ding and Ye 2009; Nigmatullina and Nelson 2006; Yan and Kou 2012), aerodynamics, polymer rheology, and electrodynamics of complex medium (Kilbas et al. 2006), image encryption (Mani et al. 2019), neural networks (Rajivganthi et al. 2018), physics (Miller and Ross 1993), chemical technology (Podlubny 1999), control of dynamical systems (Aghayan and Alfi 2020; Huong 2019; Liu et al. 2020; Tavazoei and Asemani 2020; Yen and Huong 2020). From the viewpoint of mathematics, fractional calculus generalizes integer-order calculus (Kilbas et al. 2006; Podlubny 1999).
Communicated by José Tenreiro Machado.
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Dinh Cong Huong [email protected] Department of Mathematics and Statistics, Quy Nhon University, Binh Dinh, Vietnam 0123456789().: V,-vol
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Meanwhile, fractional-order derivatives have a greater advantage in describing the memory and hereditary properties of manifold materials and processes (Gallegos and Duarte 2016; Li and Zhang 2011). It is better to describe many practical problems by fractional-order dynamical systems instead of integer-order ones (Bagley and Calico 1991; Kaslik and Sivasundaram 2012). The problem of designing state observers to estimate state vectors of dynamical systems is a central problem in many engineering applications where estimated states or outputs are required for designing control laws or monitoring system variables. There are many methods in the literature to deal with this problem for time-invariant systems (see, f
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