Finite-time \(H_{\infty}\) control for a class of Markovian jumping neural networks with distributed time varying delays-LMI approach.

*(English)*Zbl 1399.93051Summary: In this article, we investigates finite-time \(H_{\infty}\) control problem of Markovian jumping neural networks of neutral type with distributed time varying delays. The mathematical model of the Markovian jumping neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems. Finite time stability analysis for such neural networks is addressed based on the linear matrix inequality approach. Numerical examples are given to illustrate the usefulness of our proposed method. The results obtained are compared with the results in the literature to show the conservativeness.

##### MSC:

93B36 | \(H^\infty\)-control |

93C10 | Nonlinear systems in control theory |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93D20 | Asymptotic stability in control theory |

68T05 | Learning and adaptive systems in artificial intelligence |

PDF
BibTeX
XML
Cite

\textit{P. Baskar} et al., Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 2, 561--579 (2018; Zbl 1399.93051)

Full Text:
DOI

##### References:

[1] | Wang, S; Shi, T; Zeng, M, New results on robust finite-time boundedness of uncertain switched neural networks with time-varying delays, Neurocomputing, 151, 522-530, (2015) |

[2] | Syed Ali, M; Balasubramaniam, P, Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays, Chaos Solitons Fractals, 42, 2191-2199, (2009) · Zbl 1198.93192 |

[3] | Kwon, O M; Park, M J; Park, J H, Improved approaches to stability criteria for neural networks with time-varying delays, J Franklin Inst, 350, 2710-2735, (2013) · Zbl 1287.93073 |

[4] | Yu, L; Fei, S; Long, F, Multilayer neural networks-based direct adaptive control for switched nonlinear systems, Neurocomputing, 74, 481-486, (2010) |

[5] | Sun, X M; Zhao, J; Hill, D J, Stability and L_2-gain analysis for switched delay systems: A delay-dependent method, Automatica, 42, 1769-1774, (2006) · Zbl 1114.93086 |

[6] | Hou, L; Zong, G; Wu, Y, Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay, Nonlinear Anal Hybrid Systems, 5, 525-534, (2011) · Zbl 1238.93075 |

[7] | Sathy, R; Balasubramaniam, P, Stability analysis of fuzzy Markovian jumping Cohen-Grossberg BAM neural networks with mixed time-varying delays, Commun Nonlinear Sci Numer Simulat, 16, 2054-2064, (2011) · Zbl 1221.34201 |

[8] | Yao, D; Lu, Q; Wu, C; Chen, Z, Robust finite-time state estimation of uncertain neural networks with Markovian jump parameters, Neurocomputing, 159, 257-262, (2015) |

[9] | Tian, J; Li, Y; Zhao, J; Zhong, S, Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates, Appl Math Comput, 218, 5769-5781, (2012) · Zbl 1248.34123 |

[10] | Tian, J; Xiong, W; Xu, F, Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays, Appl Math Comput, 233, 152-164, (2014) · Zbl 1334.92025 |

[11] | Tian, J; Liu, Y, Improved delay-dependent stability analysis for neural networks with interval time-varying delays, Math Probl Eng, 10, (2015), Article ID 705367 · Zbl 1394.93284 |

[12] | Ren, Z; Tian, J, Improved stability analysis for neural networks with interval time-varying delays, Appl Mech Mater, 687-691, 2078-2082, (2014) |

[13] | Syed Ali, M, Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays, Neurocomputing, 149, 1280-1285, (2015) |

[14] | Chen, J; Wu, I; Lien, C, Robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay through a switching signal, J Appl Research Tec, 12, 1187-1197, (2014) |

[15] | Zeng, H B; Park, J H; Zhang, C F; Wang, W, Stability and dissipativity analysis of static neural networks with interval time-varying delay, J Franklin Inst, 352, 1284-1295, (2015) · Zbl 1307.93446 |

[16] | Wu, X; Tang, Y; Zhang, W, Stability analysis of switched stochastic neural networks with time-varying delays, Neural Networks, 51, 39-49, (2014) · Zbl 1302.93235 |

[17] | Lian, C; Zeng, Z; Yao, W; Tang, H, Multiple neural networks switched prediction for landslide displacement, Engineering Geology, 186, 91-99, (2015) |

[18] | Balasubramaniam, P; Syed Ali, M; Arik, S, Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays, Expert Syst Appl, 37, 7737-7744, (2015) |

[19] | Shi, K; Zhu, H; Zhong, S, New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach, J Franklin Inst, 352, 155-176, (2015) · Zbl 1307.93309 |

[20] | Liu, D; Zhong, S; Liu, X; Huang, Y, Stability analysis for uncertain switched neutral systems with discrete time-varying delay:a delay-dependent method, Math Comput Simulat, 80, 828-839, (2009) |

[21] | Xiang, M; Xiang, Z, Stability, L_1-gain and control synthesis for positive switched systems with time-varying delay, Nonlinear Anal Hybrid Systems, 9, 9-17, (2013) · Zbl 1287.93078 |

[22] | Sun, X; Liu, G; Wang, W; Rees, D, Stability analysis for networked control systems based on average Dwell time metheod, Internat J Robust Nonlin Cont, 20, 1774-1784, (2010) · Zbl 1204.93052 |

[23] | Branicky, M S, Multiple Lyapunov functions and other analysis tool for switched and hybrid systems, IEEE Trans Automat Control, 43, 475-482, (1998) · Zbl 0904.93036 |

[24] | Feng, W; Yang, S X; Wu, H, On robust stability of uncertain stochastic neural networks with distributed and interval time-varying delays, Chaos Solitons Fractals, 42, 2095-2104, (2009) · Zbl 1198.93158 |

[25] | Lee, S M; Kwon, O M; Park, J H, A novel delay-dependent criterion for delayed neural networks of neutral type, Phys Lett A, 374, 1843-1848, (2010) · Zbl 1236.92007 |

[26] | Zhang, Y; Shi, P; Nguang, S K; Zhang, J; Karimi, H R, Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps, Neurocomputing, 140, 1-7, (2014) |

[27] | Liberzon, D; Morse, A S, Basic problems in stability and design of switched systems, IEEE Control Syst Mag, 19, 59-70, (1999) · Zbl 1384.93064 |

[28] | Sun, Y; Wang, L; Xie, G, Delay dependent robut stability and H_∞ control for uncertain discrete-time switched systems with mode-dependent time delays, Appl Math Comput, 187, 1228-1237, (2007) · Zbl 1114.93075 |

[29] | Syed Ali, M; Saravanakumar, R, Novel delay-dependent robust H_∞ control of uncertain systems with distributed time-varying delays, Appl Math Comput, 249, 510-520, (2014) · Zbl 1338.93144 |

[30] | Lien, C H; Yu, K W, Non-fragle H_∞ control for uncertain neutral systems with time-varying delays via the LMI optimization approach, IEEE Trans Syst Man Cybernet, 37, Part B, 493-509, (2007) |

[31] | Liu, X, Stabilization of switched linear systems with mode-dependent time-varying delays, Appl Math Comput, 216, 2581-2586, (2010) · Zbl 1206.93086 |

[32] | Zhang, H; Dong, M; Wang, Y; Zhang, N, Stochastic stability analysis of neutraltype impulsive neural networks with mixed time-varying delays and Markovian jumping, Neurocomputing, 73, 2689-2695, (2010) |

[33] | Xianga, Z; Suna, Y N; Mahmoud, M S, Robust finite-time H_∞ control for a class of uncertain switched neutral systems, Commun Nonlinear Sci Numer Simul, 17, 1766-1778, (2012) · Zbl 1239.93036 |

[34] | Hong, Y; Hong, J; Xu, Y, On an output feedback finite time stabilization problem, IEEE Trans Automat Control, 46, 305-309, (2001) · Zbl 0992.93075 |

[35] | Xiang, W; Xiao, J, H_∞ finite-time control for swiched nonlinear discrete-time systems with norm-bounded disturbance, J Franklin Inst, 348, 331-352, (2011) · Zbl 1214.93043 |

[36] | Zhang, W; Fang, J; Cui, W, Exponential stability of switched genetic regulatory networks with both stable and unstable subsystems, J Franklin Inst, 350, 2322-2333, (2013) · Zbl 1293.93647 |

[37] | Lin, X; Du, H; Li, S, Finite-time boundedness and L_2-gain analysis for switched delay systems with norm-bounded disturbance, Appl Math Comput, 217, 5982-5993, (2014) · Zbl 1218.34082 |

[38] | Wang, T; Tong, S, H_∞ control design for discrete-time switched fuzzy systems, Neurocomputing, 14, 782-789, (2015) |

[39] | Li X, Lin X, Li S, Zou Y. Finite-time stability of switched nonlinear systems with finite-time unstable subsystems. J Franklin Inst, 352: 1192-1214 · Zbl 1307.93192 |

[40] | Song, Q; Wang, Z, New results on passivity analysis of uncertain neural networks with time-varying delays, Int J Comput Math, 87, 668-678, (2015) · Zbl 1186.68392 |

[41] | He, S; Liu, F, Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters, Neurocomputing, 103, 87-92, (2013) |

[42] | Wang, T; Zhao, S; Zhou, W; Yu, W, Finite-time state estimation for delayed Hopfield neural networks with Markovian jump, ISA Transactions, 57, 43-50, (2015) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.