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Consensus problem of high-order integral multi-agent systems under switchingdirected topology is considered in this study. Depending on whether the agent'sfull state is available or not, two distributed protocols are proposed toensure that states of all agents can be convergent to a same stationary value.In the proposed protocols, the gain vector associated with the agent's(estimated) state and the gain vector associated with the relative (estimated)states between agents are designed in a sophisticated way. By this particulardesign, the high-order integral multi-agent system can be transformed into afirst-order integral multi-agent system. And the convergence of the transformedfirst-order integral agent's state indicates the convergence of the originalhigh-order integral agent's state if and only if all roots of the polynomial,whose coefficients are the entries of the gain vector associated with therelative (estimated) states between agents, are in the open left-half complexplane. Therefore, many analysis techniques in the first-order integralmulti-agent system can be directly borrowed to solve the problems in thehigh-order integral multi-agent system. Due to this property, it is proved thatto reach a consensus, the switching directed topology of multi-agent system isonly required to be "uniformly jointly quasi-strongly connected", which seemsthe mildest connectivity condition in the literature. In addition, theconsensus problem of discrete-time high-order integral multi-agent systems isstudied. The corresponding consensus protocol and performance analysis arepresented. Finally, three simulation examples are provided to show theeffectiveness of the proposed approach.

Reaching a Consensus in Networks of High-Order Integral Agents under Switching Directed Topology