Leader-Following Output Feedback <i>H</i>_∞ Consensus of Fractional-Order Multi-Agent Systems with Input Saturation

Abstract

This paper investigates the leader-following H∞ consensus of fractional-order multi-agent systems (FOMASs) under input saturation via the output feedback. Based on the bounded real lemma for FOSs, the sufficient conditions of H∞ consensus for FOMASs are provided in α∈0,1 and 1,2, respectively. Furthermore, the iterative linear matrix inequalities (ILMIs) approaches are applied for solving quadratic matrix inequalities (QMIs). The ILMI algorithms show a method to derive initial values and transform QMIs into LMIs. Mathematical tools are employed to transform the input saturation issue into optimal solutions of LMIs for estimating stable regions. The ILMI algorithms avoid the conditional constraints on matrix variables during the LMIs’ construction and reduce conservatism. The approach does not disassemble the entire MASs by transformations to the Laplacian matrix, instead adopting a holistic analytical perspective to obtain gain matrices. Finally, numerical examples are conducted to validate the efficiency of the approach.

Keywords

• fractional-order multi-agent systems
• <i>H</i>_∞ control
• static output feedback
• iterative linear matrix inequality