Finite-time boundedness of Markovain jump nonlinear systems with incomplete information

• Published in: International journal of systems science Vol. 49; no. 16; pp. 3296 - 3306
• Main Authors: Zhang, Yingqi, Yang, Yang, Shi, Peng, Pan, Jeng-Shyang
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 10.12.2018; Taylor & Francis Ltd
• Subjects: boundedness; Dynamical systems; H_{\infty }; incomplete transition probabilities; Linear matrix inequalities; Markov processes; Markovian jump nonlinear systems; Mathematical analysis; Matrix methods; Nonlinear dynamics; Nonlinear systems; stochastic finite-time; stochastic finite-time boundedness; Transition probabilities
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2018.1536235

This paper deals with the finite-time $ H_{\infty } $ H ∞ bounded control problem of a class of uncertain Markovian jump nonlinear systems with partially unknown transition probabilities and norm-bounded disturbances. The purpose of the paper is to derive a stochastic finite-time controller such that the resulting nominal or uncertain stochastic nonlinear model is stochastically finite-time $ H_{\infty } $ H ∞ bounded by applying stochastic analysis techniques and free connection weighting matrix approach. We also provide stochastic finite-time stability and stochastic finite-time boundedness criteria of the class of nominal or uncertain stochastic nonlinear dynamics. Moreover, the derived criteria can be simplified into linear matrix inequalities (LMIs), which could be solved by employing Matlab LMI toolbox. Finally, the effectiveness of proposed approaches is demonstrated by a practical example.