研究具有切换有向拓扑和非对称时变时滞的高阶多智能体系统的一致性问题. 通过引入正交线性变换和Lyapunov-Krasovskii泛函方法, 依据线性矩阵不等式给出了系统解决一致性问题的充分条件以及可容许时变时滞的上界估计. 其主要贡献是基于Lyapunov方程和代数不等式建立了协议参数的显性设计, 该参数设计形式简单且易于计算, 并保证了所给充分条件中线性矩阵不等式的可解性, 使得高阶多智能体系统的一致性在切换有向拓扑下对非对称时变时滞是鲁棒的.

This paper focuses on the consensus problem for high-order multi-agent systems with switching directed topologies and asymmetric time-varying communication delays. By introducing an orthogonal linear transformation and Lyapunov-Krasovskii functional approach, we establish some sufficient conditions for consensus convergence and the maximum allowable upper bounds of time-varying delays, which are characterized by linear matrix inequalities. The main contribution of this paper is that the explicit design of protocol parameters is provided based on Lyapunov equation and algebraic inequality, which is simple in form and easy to compute. The design guarantees the solvability of the linear matrix inequalities in the sufficient conditions and the robust consensus with respect to asymmetric time-varying delays for high-order multi-agent systems.