Robust stability, stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters
Robust stability, stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters
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DOI：
10.1002/rnc.744
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发表时间：
2003-07
影响因子：
3.9
通讯作者：
M. Mahmoud;P. Shi
中科院分区：
文献类型：
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作者：
M. Mahmoud;P. Shi
研究了一类具有马尔可夫跳变参数的不确定时滞系统的随机稳定性与镇定问题。跳跃参数被建模为连续时间、离散状态的马尔可夫过程。假设参数不确定性是真实的，时变和范数有界的，出现在状态，输入和延迟状态矩阵。时间延迟因子是常数且未知，具有已知的界限。对于标称和不确定时滞跳变系统，给出了时滞独立和时滞相关的随机稳定性准则的完整结果。控制目标是设计一个状态反馈控制器，以保证随机稳定性和指定的∞性能。我们建立了具有和不具有不确定参数的时滞马尔可夫跳变系统的控制问题本质上可以用一组有限的耦合代数Riccati不等式或线性矩阵不等式的解来解决。扩展的结果不确定的跳跃率的情况下，也提供了。版权所有© 2003年约翰威利父子有限公司。
In this paper, the problems of stochastic stability and stabilization for a class of uncertain time‐delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process. The parametric uncertainties are assumed to be real, time‐varying and norm‐bounded that appear in the state, input and delayed‐state matrices. The time‐delay factor is constant and unknown with a known bound. Complete results for both delay‐independent and delay‐dependent stochastic stability criteria for the nominal and uncertain time‐delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed ℋ∞‐performance are guaranteed. We establish that the control problem for the time‐delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided. Copyright © 2003 John Wiley & Sons, Ltd.