Exponential Stability Using Sliding Mode Control for Stochastic Neutral-Type Systems

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.

[1]  Zhiyu Xi,et al.  A New Design of Robust ${\rm H}_{\infty}$ Sliding Mode Control for Uncertain Stochastic T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

[2]  Jinde Cao,et al.  Event-Triggered Synchronization for Neutral-Type Semi-Markovian Neural Networks With Partial Mode-Dependent Time-Varying Delays , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Peng Shi,et al.  Adaptive synchronization of delayed Markovian switching neural networks with Lévy noise , 2015, Neurocomputing.

[4]  Tsachy Weissman,et al.  Relations Between Information and Estimation in Discrete-Time Lévy Channels , 2014, IEEE Transactions on Information Theory.

[5]  Yao Wang,et al.  Exponential Synchronization of Chaotic Systems with Stochastic Perturbations via Quantized Feedback control , 2019, Circuits, Systems, and Signal Processing.

[6]  Jinde Cao,et al.  New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters , 2018, J. Frankl. Inst..

[7]  Cong Xu,et al.  Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays , 2020 .

[8]  Chunmei Zhang,et al.  Graph Theory-Based Approach for Stability Analysis of Stochastic Coupled Systems With Lévy Noise on Networks , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Yonggui Kao,et al.  A sliding mode approach to H∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems , 2015, Autom..

[10]  Junyong Zhai,et al.  Dynamic Output-Feedback Control for Nonlinear Time-Delay Systems and Applications to Chemical Reactor Systems , 2019, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Yuhua Xu,et al.  Adaptive Exponential State Estimation for Markovian Jumping Neural Networks with Multi-delays and Lévy Noises , 2019, Circuits Syst. Signal Process..

[12]  Yonggui Kao,et al.  H∞ sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters , 2015, Inf. Sci..

[13]  Yang Shi,et al.  New Results on Sliding-Mode Control for Takagi–Sugeno Fuzzy Multiagent Systems , 2019, IEEE Transactions on Cybernetics.

[14]  Yuhua Xu,et al.  Multi-Delay-Dependent Exponential Synchronization for Neutral-Type Stochastic Complex Networks with Markovian Jump Parameters via Adaptive Control , 2018, Neural Processing Letters.

[15]  Chunyu Yang,et al.  Integral Sliding Mode Control for Singularly Perturbed Systems with Mismatched Disturbances , 2018, Circuits Syst. Signal Process..

[16]  Y. C. Chong,et al.  On the Measurement and Modeling of the Heat Transfer Coefficient of a Hollow-Shaft Rotary Cooling System for a Traction Motor , 2018, IEEE Transactions on Industry Applications.

[17]  James Lam,et al.  Stability analysis of linear stochastic neutral-type time-delay systems with two delays , 2018, Autom..

[18]  Peng Shi,et al.  Exponential Stability of Markovian Jumping Systems via Adaptive Sliding Mode Control , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[19]  Yuqing Sun,et al.  Adaptive exponential stabilization of neutral-type neural network with Lévy noise and Markovian switching parameters , 2018, Neurocomputing.

[20]  Yuguang Fang,et al.  Preserving Model Privacy for Machine Learning in Distributed Systems , 2018, IEEE Transactions on Parallel and Distributed Systems.

[21]  Wuneng Zhou,et al.  Topology identification of complex delayed dynamical networks with multiple response systems , 2017 .

[22]  Hui Zhou,et al.  Synchronization of Stochastic Lévy Noise Systems on a Multi-Weights Network and Its Applications of Chua’s Circuits , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Jianbin Qiu,et al.  Adaptive Fuzzy Sliding Mode Control for Network-Based Nonlinear Systems With Actuator Failures , 2018, IEEE Transactions on Fuzzy Systems.

[24]  Shouming Zhong,et al.  Simultaneous Finite-Time Control and Fault Detection for Singular Markovian Jump Delay Systems with Average Dwell Time Constraint , 2018, Circuits Syst. Signal Process..

[25]  Ligang Wu,et al.  Observer-based adaptive sliding mode control for nonlinear Markovian jump systems , 2016, Autom..

[26]  Jun Zhou,et al.  Master‐slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation , 2018 .

[27]  Peng Shi,et al.  Adaptive Synchronization for Neutral-Type Neural Networks with Stochastic Perturbation and Markovian Switching Parameters , 2014, IEEE Transactions on Cybernetics.

[28]  Yugang Niu,et al.  Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities , 2018, Autom..

[29]  Jun Yang,et al.  Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control , 2015, Commun. Nonlinear Sci. Numer. Simul..

[30]  Yuhua Xu,et al.  Adaptive State Estimation of Stochastic Delayed Neural Networks with Fractional Brownian Motion , 2018, Neural Processing Letters.

[31]  Jang Gyu Lee,et al.  Robust stability and stabilization of linear delayed systems with structured uncertainty , 1999, Autom..

[32]  Jun Yang,et al.  pth Moment synchronization of Markov switched neural networks driven by fractional Brownian noise , 2016, Neural Computing and Applications.

[33]  Khac Duc Do,et al.  Inverse optimal control of stochastic systems driven by Lévy processes , 2019, Autom..

[34]  Ligang Wu,et al.  Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Jun Zhou,et al.  Almost sure adaptive asymptotically synchronization for neutral-type multi-slave neural networks with Markovian jumping parameters and stochastic perturbation , 2016, Neurocomputing.

[36]  Quanyan Zhu,et al.  Adaptive Exponential Synchronization of Multislave Time-Delayed Recurrent Neural Networks With Lévy Noise and Regime Switching , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Peng Shi,et al.  Exponential Synchronization for Markovian Stochastic Coupled Neural Networks of Neutral-Type via Adaptive Feedback Control , 2017, IEEE Transactions on Neural Networks and Learning Systems.