Abstract
This paper studies consensus problems for multi-agent systems modeled by linear time-invariant systems with external disturbances under a fixed directed communication topology. It is shown that consensus can be achieved if each agent with the same disturbance signals. But the result is different for each agent with different disturbances. In this case, the finite-gain Lp consensus is introduced to describe the effects of the external disturbance on the consensus performance. A necessary and sufficient condition for reaching finite-gain Lp consensus is presented, and analytic estimation of the Lp gain is given. A distributed algorithm is proposed to ensure that the finite-gain L2 consensus can be reached with a desired L2 gain. Numerical examples are given to illustrate the given results.
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