Stability Analysis for T-S Fuzzy Semi-Markovian Switching CVNs with Mixed Delays and General Uncertain Transition Rates

This paper concerns with the stochastic stability problem for Takagi-Sugeno (T-S) fuzzy semi-Markovian switching complex-valued networks (CVNs) with mixed delays, where the transition rates of the semi-Markovian process are in the general uncertain form which contain two cases: completely unknown or unknown but with known upper/lower bounds. Based on the Lyapunov stability theory and the stochastic analysis technique, several mode-dependent stability criteria are established to guarantee the considered T-S fuzzy CVN to be asymptotically stable in the mean-square sense. Finally, one numerical example is provided to demonstrate feasibility of the obtained theoretical results.

[1]  Jigui Jian,et al.  Global exponential convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects , 2017, Fuzzy Sets Syst..

[2]  Shaocheng Tong,et al.  Adaptive Fuzzy Tracking Control Design for SISO Uncertain Nonstrict Feedback Nonlinear Systems , 2016, IEEE Transactions on Fuzzy Systems.

[3]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Yang Liu,et al.  Dynamic Output Feedback Control for Continuous-Time T–S Fuzzy Systems Using Fuzzy Lyapunov Functions , 2017, IEEE Transactions on Fuzzy Systems.

[5]  Hao Shen,et al.  Generalised state estimation of Markov jump neural networks based on the Bessel–Legendre inequality , 2019, IET Control Theory & Applications.

[6]  Jun Cheng,et al.  New results on stabilization analysis for fuzzy semi-Markov jump chaotic systems with state quantized sampled-data controller , 2020, Inf. Sci..

[7]  Yonggui Kao,et al.  Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems With Generally Uncertain Transition Rates , 2018, IEEE Transactions on Automatic Control.

[8]  Yang Shi,et al.  Stochastic stability and robust stabilization of semi‐Markov jump linear systems , 2013 .

[9]  Jiaowan Luo,et al.  Stochastic stability of linear systems with semi-Markovian jump parameters , 2005, The ANZIAM Journal.

[10]  Min Wu,et al.  Hidden Markov Model Based Fault Detection for Networked Singularly Perturbed Systems , 2020 .

[11]  W. T. Yeung,et al.  Damage detection in bridges using neural networks for pattern recognition of vibration signatures , 2005 .

[12]  Jun Wang,et al.  Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Tohru Nitta,et al.  Solving the XOR problem and the detection of symmetry using a single complex-valued neuron , 2003, Neural Networks.

[14]  Quanxin Zhu,et al.  Stability analysis of semi-Markov switched stochastic systems , 2018, Autom..

[15]  Jinde Cao,et al.  A Fuzzy Lyapunov Function Approach to Positive Ll Observer Design for Positive Fuzzy Semi-Markovian Switching Systems With Its Application , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[16]  Xian Zhang,et al.  Exponential Stability Analysis for Delayed Semi-Markovian Recurrent Neural Networks: A Homogeneous Polynomial Approach , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Jun Cheng,et al.  A sojourn probability approach to fuzzy-model-based reliable control for switched systems with mode-dependent time-varying delays☆ , 2017 .

[18]  Zhongjie Wang,et al.  Stability of Markovian jump systems with generally uncertain transition rates , 2013, J. Frankl. Inst..

[19]  R. Ramaswami,et al.  Book Review: Design and Analysis of Fault-Tolerant Digital Systems , 1990 .

[20]  Grienggrai Rajchakit,et al.  Exponential stability of semi-Markovian jump generalized neural networks with interval time-varying delays , 2016, Neural Computing and Applications.

[21]  Fuad E. Alsaadi,et al.  Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays , 2018, Neural Networks.

[22]  Zhi-Hua Zhou,et al.  Multilabel Neural Networks with Applications to Functional Genomics and Text Categorization , 2006, IEEE Transactions on Knowledge and Data Engineering.

[23]  Akira Hirose,et al.  Recent Progress in Applications of Complex-Valued Neural Networks , 2010, ICAISC.