一类二维Markov跳跃非线性时滞系统的镇定控制

赵 平;康 宇

系统科学与数学 ›› 2007, Vol. 27 ›› Issue (3) : 451-463.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2007, Vol. 27 ›› Issue (3) : 451-463. DOI: 10.12341/jssms09479
论文

一类二维Markov跳跃非线性时滞系统的镇定控制

    赵 平, 康 宇
作者信息 +

Stabilization Control for a Class of Two-Dimensional MarkovianJumping Nonlinear Systems with Time-Delays

    Zhao Ping, Kang Yu
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摘要

研究一类二维Markov跳跃非线性时滞系统的镇定控制问题. 给出了Markov跳跃非线性时滞系统解的存在唯一性的一个充分条件,以及系统依概率全局渐近稳定的判别准则. 通过构造适当形式的Lyapunov函数,采用积分反推方法给出了一类二维Markov跳跃非线性时滞系统的无记忆状态反
馈控制器. 证明了在该控制律的作用下,闭环系统平衡点依概率全局渐近稳定.

Abstract

In this paper, stabilization control problem for a class of two dimensional Markovian jumping nonlinear systems with time-delays is investigated. A
sufficient condition of existence and uniqueness of the solution process to Markovian jumping nonlinear systems is given. And, a criterion for asymptotical stability in probability is obtained. Through properly constructing Lyapunov function and using the backstepping method, a memoryless state-feedback controller is designed. It is shown that the equilibrium of the closed-loop system is globally asymptotically stable in probability.

关键词

非线性系统 / Markov跳跃系统 / 时滞系统 / 积分反推方法 / 镇定控制.

Key words

Nonlinear system / markovian jumping system / time-delay system / backstepping method / stabilization control.

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赵 平 , 康 宇. 一类二维Markov跳跃非线性时滞系统的镇定控制 . 系统科学与数学, 2007, 27(3): 451-463. https://doi.org/10.12341/jssms09479
Zhao Ping , Kang Yu. Stabilization Control for a Class of Two-Dimensional MarkovianJumping Nonlinear Systems with Time-Delays. Journal of Systems Science and Mathematical Sciences, 2007, 27(3): 451-463 https://doi.org/10.12341/jssms09479
中图分类号： 34A34    60J05   
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