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首页> 外文期刊>IEEE Transactions on Automatic Control >Descriptor Discretized Lyapunov Functional Method: Analysis and Design
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Descriptor Discretized Lyapunov Functional Method: Analysis and Design

机译：描述符离散Lyapunov函数方法：分析和设计

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摘要

Stability and state-feedback stabilization of linear systems with uncertain coefficients and uncertain time-varying delays are considered. The system under consideration may be unstable without delay, but it becomes asymptotically stable for positive values of the delay. A new descriptor discretized Lyapunov-Krasovskii functional (LKF) method is introduced, which combines the application of the complete LKF and the discretization method of K. Gu with the descriptor model transformation. For the first time, the new method allows to apply the discretized LKF method to synthesis problems. Moreover, the analysis of systems with polytopic time-invariant uncertainties is less restrictive by the new discretized method. Sufficient conditions for robust stability and stabilization of uncertain neutral type systems are derived in terms of linear matrix inequalities (LMIs) via input-output approach to stability. Numerical examples illustrate the efficiency of the new method.
机译：考虑具有不确定系数和不确定时变时滞的线性系统的稳定性和状态反馈稳定。所考虑的系统可能会没有延迟而变得不稳定，但是对于正值的延迟，它变得渐近稳定。介绍了一种新的描述子离散化Lyapunov-Krasovskii泛函（LKF）方法，该方法将完整的LKF的应用和K. Gu的离散化方法与描述子模型转换相结合。新方法首次允许将离散LKF方法应用于综合问题。此外，采用新的离散化方法，对具有多时不变性不确定性的系统的分析限制较少。通过输入-输出方法求线性稳定性，根据线性矩阵不等式（LMI）得出不确定中立型系统鲁棒稳定性和稳定性的充分条件。数值算例说明了该新方法的有效性。

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