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**Neural-network-based finite-time \(H_\infty\) control for extended Markov jump nonlinear systems.**
*(English)*
Zbl 1200.93125

Summary: This paper presents a neural-network-based finite-time \(H_\infty\) control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. Sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed-loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed \(H_\infty\) noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results.

### MSC:

93E03 | Stochastic systems in control theory (general) |

93C10 | Nonlinear systems in control theory |

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

60J75 | Jump processes (MSC2010) |

### Keywords:

Markov jump systems; nonlinearities; finite-time stabilization; \(H_\infty\) control; transition probabilities; neural networks
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\textit{X. Luan} et al., Int. J. Adapt. Control Signal Process. 24, No. 7, 554--567 (2010; Zbl 1200.93125)

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