D-stability performance analysis and stabilization of Sun-Earth L₂ formation flying system

This paper investigates the problem of D-stability performance of an L₂ point formation control system with parametric uncertainties. A Quasi linear parameter varying (QLPV) model is introduced for the L₂ point formation flying, based on which a nonlinear control strategy is developed via the polynomial eigenstructure assignment (PEA) approach. The designed controller can guarantee the closed-loop system with invariant performance over a wide range of conditions due to its special structure with varying parameters. The robust D-stability of the multiple input and multiple output (MIMO) system is also addressed. It is shown that the D-stability performance of the L₂ point formation control system with parametric uncertainties can be ensured by using PEA controller. Finally, a simulation of formation flying is performed to illustrate the effectiveness of the proposed control approach.