Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

Zhao Jing Wu; Xue Jun Xie; Peng Shi; Yuan qing Xia

doi:10.1016/j.automatica.2008.12.002

Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

Zhao Jing Wu^*, Xue Jun Xie, Peng Shi, Yuan qing Xia

^*Corresponding author for this work

School of Automation

Research output: Contribution to journal › Article › peer-review

279 Citations (Scopus)

Abstract

A more general class of stochastic nonlinear systems with irreducible homogenous 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.

Original language	English
Pages (from-to)	997-1004
Number of pages	8
Journal	Automatica
Volume	45
Issue number	4
DOIs	https://doi.org/10.1016/j.automatica.2008.12.002
Publication status	Published - Apr 2009

Keywords

Backstepping
Markovian switching
Nonlinear stochastic systems

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10.1016/j.automatica.2008.12.002

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title = "Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching",

abstract = "A more general class of stochastic nonlinear systems with irreducible homogenous 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.",

keywords = "Backstepping, Markovian switching, Nonlinear stochastic systems",

author = "Wu, \{Zhao Jing\} and Xie, \{Xue Jun\} and Peng Shi and Xia, \{Yuan qing\}",

year = "2009",

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doi = "10.1016/j.automatica.2008.12.002",

language = "English",

volume = "45",

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T1 - Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

AU - Wu, Zhao Jing

AU - Xie, Xue Jun

AU - Shi, Peng

AU - Xia, Yuan qing

PY - 2009/4

Y1 - 2009/4

N2 - A more general class of stochastic nonlinear systems with irreducible homogenous 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.

AB - A more general class of stochastic nonlinear systems with irreducible homogenous 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.

KW - Backstepping

KW - Markovian switching

KW - Nonlinear stochastic systems

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U2 - 10.1016/j.automatica.2008.12.002

DO - 10.1016/j.automatica.2008.12.002

M3 - Article

AN - SCOPUS:61849124772

SN - 0005-1098

VL - 45

SP - 997

EP - 1004

JO - Automatica

JF - Automatica

IS - 4

ER -

Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

Abstract

Keywords

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