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**Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching.**
*(English)*
Zbl 1162.93044

Summary: A more general class of stochastic nonlinear systems with irreducible homogeneous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case.

### MSC:

93E15 | Stochastic stability in control theory |

60J75 | Jump processes (MSC2010) |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93B52 | Feedback control |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

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\textit{Z.-J. Wu} et al., Automatica 45, No. 4, 997--1004 (2009; Zbl 1162.93044)

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