Interval observers for linear functions of states and unknown inputs of nonlinear fractional-order systems with time del
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Interval observers for linear functions of states and unknown inputs of nonlinear fractional-order systems with time delays Dinh Cong Huong1,2 · Dao Thi Hai Yen3 Received: 14 February 2020 / Revised: 13 April 2020 / Accepted: 9 May 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract The main objective of this paper is to design interval observers using the output signals and the delayed output signals to estimate the state vector and unknown input vector of nonlinear fractional-order systems with time delay. We first propose and design two new functional observers, such that they bound the set of all admissible values of a linear function of the state vector and the unknown input vector at each instant of time. We then derive conditions for the existence of interval functional observers and provide an effective design algorithm for computing unknown observer matrices. Finally, an example is given to show the effectiveness of the proposed design approach. Keywords Nonlinear fractional-order systems · Functional interval observers · Linear programming Mathematics Subject Classification 34H05 · 93B07 · 93B51
1 Introduction Fractional calculus (a generalization of the ordinary differentiation and integration) has been a well-known topic, since it has played an important role in industrial applications, particularly in chemical reactions, biological systems Moaddy et al. (2012), image encryption Mani et al. (2019), information processing Feki (2012), electronics Radwan et al. (2003), and with memristors Radwan et al. (2011). It has been shown that in many applications, fractional
Communicated by Agnieszka Malinowska.
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Dinh Cong Huong [email protected] Dao Thi Hai Yen [email protected]
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Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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Department of Sciences, Phu Yen University, Phu Yen, Vietnam 0123456789().: V,-vol
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derivative-based models provide more accurate solutions for real processes of anomalous systems than the integer-order derivative-based models do Baleanu et al. (2012) and Yang (2017). Recently, it has also been proved that fractional differential equations have gained considerable popularity and importance due to their numerous applications in many fields of science and engineering including chaotic dynamics, material sciences, mechanic of fractal and complex media, quantum mechanics, physical kinetics, chemistry, biology, economics, and control theory Machado et al. (2011). In particular, a fractional generalization of the Newtonian equation to describe the dynamics of complex phenomena Baleanu et al. (2010), fractional-order Cohen-Grossberg BAM neural networks with time delays Rajivganthi et al. (2018), a fractional Langevin equation, with applications in polymer layers Baleanu et al. (2010), and fractional mathematical models describing
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