ℋ∞ consensus synthesis of multiagent systems with nonuniform time-varying input delays: A dynamic IQC approach

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In this chapter, we consider the problem of ℋ∞ consensus control of a class of weakly heterogeneous multiagent systems (MASs) subject to nonuniform time-varying input delays. The MAS is considered to be weakly heterogeneous in the sense that all the agents’ system matrices (except the “A” matrix) are nonidentical. A unifying scheme is proposed under the integral quadratic constraint (IQC) framework for both state- and output-feedback distributed control synthesis. Novel distributed observer-based delay control protocols are constructed using not only the relative estimation states from neighboring agents but also the local real-time information of time delays from the agent itself. It is shown that the consensus performance can be reached by solving the ℋ∞ stabilization problems for a set of independent linear fractional transformation systems, whose dimensions are equal to that of a single-agent plant plus the associated local IQC dynamics. Furthermore, the synthesis conditions guaranteeing optimal ℋ∞ consensus performance for both state- and output-feedback cases are formulated in terms of linear matrix inequalities, which can be solved effectively via convex optimization. A numerical example has been used to demonstrate the proposed approach.

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Stability, Control and Application of Time-Delay Systems