This paper is concerned with stability and ${\mathcal{H}}_2$ analysis of periodic discrete-time uncertain systems. New conditions based on structured Lyapunov functions are provided in the form of parameter-dependent Linear Matrix Inequalities (LMIs). The Lyapunov functions make use of the periodic dynamic of the system to provide less conservative results in terms of scalar decision variables, LMI rows and ${\mathcal{H}}_2$ guaranteed cost. The proposed techniques are necessary and sufficient conditions to certify the stability of periodic discrete-time uncertain systems. Numerical experiments illustrate the improvement granted by the methods proposed in this paper over existing techniques.

中文翻译：

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通过结构化Lyapunov函数分析周期离散不确定系统的稳定性和鲁棒性能

本文涉及稳定性和 ${\mathcal{H}}_2$离散时间不确定系统的分析。基于结构化Lyapunov函数的新条件以依赖于参数的线性矩阵不等式（LMI）的形式提供。Lyapunov函数利用系统的周期性动力，在标量决策变量，LMI行和${\mathcal{H}}_2$保证成本。所提出的技术是证明周期性离散时间不确定系统稳定性的必要和充分条件。数值实验说明了本文提出的方法对现有技术的改进。