Exponential Stability Using Sliding Mode Control for Stochastic Neutral-Type Systems
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Exponential Stability Using Sliding Mode Control for Stochastic Neutral-Type Systems Qiaoyu Chen1,3 · Dongbing Tong2 Jinping Mou5
· Wuneng Zhou3 · Yuhua Xu4 ·
Received: 9 February 2020 / Revised: 29 September 2020 / Accepted: 6 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This study deals with the exponential stability of stochastic neutral-type systems (SNTSs) with Markovian switching and Lévy noises. A new integral sliding mode surface for SNTSs is constructed to design a sliding mode controller. Furthermore, a new Lyapunov function is assigned to obtain the exponential stability criterion of SNTSs. On this basis, a new sliding mode control law is proposed to ensure the accessibility of SNTSs. In addition, the parameters of the sliding mode controller for SNTSs are obtained. Finally, an example to illustrate the theoretical results has been presented. Keywords Sliding mode control · Lévy noises · Exponential stability · Sliding mode surface · Stochastic neutral-type systems
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Dongbing Tong [email protected] Wuneng Zhou [email protected] Qiaoyu Chen [email protected] Yuhua Xu [email protected] Jinping Mou [email protected]
1
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
2
School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
3
College of Information Sciences and Technology, Donghua University, Shanghai 200051, China
4
School of Finance, Nanjing Audit University, Jiangsu 211815, China
5
School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, China
Circuits, Systems, and Signal Processing
1 Introduction The current state of systems is dependent on the state attained during the previous event. Numerous mathematical models of systems that reflect the real world are established based on neutral-type equations, including delays of the states and their derivatives. In addition, neutral-type phenomena are frequently observed in the studies of distributed systems and dynamic processes, such as heat exchanges, microwave oscillators, and population ecology. Recently, the stability and synchronisation control problems of neutral-type systems have received widespread attention [1,5,7,15,18,28]. In [1], using the M-matrix method and algebraic inequalities, an adaptive exponential synchronisation criterion was studied for neutral-type networks, and sufficient conditions were developed with an adaptive feedback controller. In [15], a few passive filters were obtained for neutral-type networks using optimisation techniques. Additionally, many systems are often subject to abrupt changes in their parameters for a myriad of reasons such as changes in subsystem interconnections and component failures. These changes can be described by Markovian switching systems based on the Markov chain, which is only related to the time interval. This system has been widely discussed and studied. Markovian switc
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