Modified Order-Reduction Method for Distributed Control of Multi-Spacecraft Networks With Time-Varying Delays

This paper studies the order-reduction method for robust distributed control of multi-spacecraft formation problems considering external disturbance and time-varying delays. Two kinds of delay-dependent controllers are designed to achieve accompanying flight and around flight, respectively. Further, a modified order-reduction method is proposed to reduce the order of sufficient conditions in the form of linear matrix inequalities (LMIs), which guarantee the desired relative state between the controlled spacecraft and the reference point subject to $\boldsymbol{H}_{\infty}$ performance. Numerical simulations are provided to illustrate the effectiveness of theoretical results and show that the proposed modified order-reduction method can significantly reduce the numerical complexity of LMIs compared with existing ones.

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