SCIENCE CHINA Information Sciences, Volume 61, Issue 9: 092206(2018) https://doi.org/10.1007/s11432-017-9255-2

## Cooperative output regulation for linear uncertain MIMO multi-agent systems by output feedback

• AcceptedSep 22, 2017
• PublishedMay 22, 2018
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### Abstract

In this paper, we study the cooperative output regulation problem for a class of general linear uncertain multi-input multi-output (MIMO) multi-agent systems subject toa well-defined vector relative degree. By proposing some suitable internal model, the problem is first converted into the auxiliary cooperative stabilization problem of the augmented system in the so-called strict feedback normal form. This auxiliary problem is then solved by some developed robust control techniques, such as multiple high-gain feedback and mixed distributed observer, leading to an effective distributed output feedback regulator synthesis for the original cooperative output regulation problem.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61403082) and Natural Science Foundation of Fujian Province (Grant No. 2016J06014).

### References

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• Figure 1

The digraph $\bar{\mathcal{G}}_i$.

•

Algorithm 1 Synthesis for distributed output feedback controller 10

Output:Assumptions zy-ass-01 and zy-ass-02 hold for systems 1 and 2.

Find the minimum polynomial of $S$ and determine the matrix $\Phi,~\Gamma$;

{by 5}

Find any controllable pair $M$ and $Q$;

{by the Hurwitz matrix $M$}

Get $T$ and $\Psi=\Gamma~T^{-1}$;

{by solving $T\Phi-MT=Q\Gamma$}

Define the internal model and form the augmented system;

{by 6 and 7}

Determine the distributed state feedback gain $K_i$;

{by 19}

Determine the observer gains $h_i$ and $\tau_i$ in sequence;

{by 32 and 33}

Find matrices $G_{1i},~G_{2i},~G_{3i},~G_{4i}$.

{by 34 and 35}

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