Output-feedback H<inf>∞</inf> consensus of linear multi-agent systems over general directed graphs

Abstract

This paper studies the design of dynamic outputfeedback protocols for H ∞ consensus of homogeneous linear multi-agent systems over general directed graphs. Except for the consensus objective when no disturbance exists, the design protocol is also expected to guarantee an H ∞ norm level of the error system from disturbances to the error signal. The H ∞ consensus problem is first transformed into an H ∞ outputfeedback control problem of a reduced-order system. Then based on the bound real lemma, a sufficient condition in terms of a Riccati equation and two linear matrix inequalities is derived for the existence of a desired output-feedback protocol. Compared with the existing results, the proposed design method can deal with output-feedback H ∞ consensus over general directed graphs containing a spanning tree, which is illustrated by a numerical example.