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**Observer-type consensus protocol for a class of fractional-order uncertain multiagent systems.**
*(English)*
Zbl 1253.93095

Summary: We investigate the consensus problem for a class of fractional-order uncertain multiagent systems with general linear node dynamics. Firstly, an observer-type consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on property of the Kronecker product and stability theory of fractional-order system, some sufficient conditions are presented for robust asymptotical stability of the observer-based fractional-order control systems. Thirdly, robust stabilizing controllers are derived by using linear matrix inequality approach and matrix’s singular value decomposition. Our results are in the form of linear matrix inequalities which can easily be solved by LMI toolbox in MATLAB. Finally, a numerical simulation is performed to show the effectiveness of the theoretical results.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

34A08 | Fractional ordinary differential equations |

34H05 | Control problems involving ordinary differential equations |

### Keywords:

robust asymptotical stability; fractional-order control systems; linear matrix inequality; singular value decomposition; LMI toolbox; MATLAB
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\textit{H. Li}, Abstr. Appl. Anal. 2012, Article ID 672346, 18 p. (2012; Zbl 1253.93095)

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### References:

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