离散时间高阶不确定线性多个体系统保性能一致性分析

摘要

本文研究了存在参数不确定性的离散时间高阶多个体系统保性能一致性问题，给出了一种设计其线性一致性协议的方法。首先，通过模型转换的方法将该问题转换为一组离散时间不确定系统的稳定性问题；然后，构造合适的Lyapunov函数并利用离散时间系统稳定性理论，推导出一个使离散时间高阶不确定多个体系统获得保性能一致的LMI充分条件；接着，以一致性序列的形式给出参数不确定条件下的离散时间高阶多个体系统的一致性收敛结果。最后，参数不确定的对比数值仿真验证了本文理论的正确性和有效性。%A guaranteed cost consensus problem of discrete-time high-order linear multi-agent systems with parameter uncertainties is studied, and a linear consensus protocol of it is designed in this paper. Firstly, the consensus problem is transformed into a stability problem of a group of general discrete-time uncertain linear systems via a model transformation method. Secondly, by constructing a suitable Lyapunov function and using the stability theory of discrete-time linear sys-tems, a sufficient LMI condition is derived to insure that the discrete-time high-order uncertain linear multi-agent systems achieve guaranteed cost consensus. Thirdly, convergence results are given as consensus function sequences of discrete-time high-order linear multi-agent systems with parameter uncertainties. Finally, a contrast numerical experiment with uncertain parameters is provided to demonstrate the correctness and effectiveness of the theoretical results.