Admissibility analysis and control synthesis for descriptor systems with random abrupt changes
Admissibility analysis and control synthesis for descriptor systems with random abrupt changes
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DOI：
10.1016/j.amc.2013.03.058
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发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
Srimanta Santra
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文献类型：
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作者：
Srimanta Santra
研究了一类具有马尔可夫跳变参数的不确定广义时滞系统的容许性分析和状态反馈鲁棒控制器设计问题。特别地，延迟因子被假定为属于给定区间的时变，并且参数不确定性被假定为时变但范数有界。利用线性矩阵不等式优化方法和时滞分割技术，得到了一组新的时滞相关的充分条件，保证了不确定广义系统正则、无脉冲和随机稳定.进一步，针对存在容许参数不确定性和随机突变的不确定广义系统，设计了一种具有适当增益控制矩阵的静态鲁棒控制器，实现了系统的鲁棒镇定。通过考虑时变时滞与其上下界之间的关系，以线性矩阵不等式的形式给出了状态反馈控制存在的一组新的充分条件，并利用MATLAB的线性矩阵不等式工具箱进行了求解.更准确地说，当这些LMI是可行的，所需的静态鲁棒控制的表达式将被确定。数值算例和仿真结果表明，所得结果显著改善了已有结果的时滞容许上界。
This article addresses the admissibility analysis and state-feedback robust control synthesis problem for a class of uncertain descriptor systems with time delays and Markovian jumping parameters. In particular, the delay factor is assumed to be time varying which belongs to a given interval and parameter uncertainties are assumed to be time-varying but norm bounded. By implementing linear matrix inequality optimization approach together with delay fractioning technique, a new set of delay dependent sufficient condition is derived which guarantees that the uncertain singular system to be regular, impulse-free and stochastically stable. Further, a static robust control design with an appropriate gain control matrix has been derived to achieve the robust stabilization for uncertain singular systems in the presence admissible parameter uncertainties and random abrupt changes. By considering the relationship among the time varying delay and its lower and upper bounds, a new set of sufficient conditions are established for the existence of state feedback control in terms of LMIs, which can be efficiently solved via MATLAB LMI toolbox. More precisely, when these LMIs are feasible, an expression of a desired static robust control will be determined. Further, numerical examples with simulation result are given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.