H_∞ Control of Flexible Spacecraft with Disturbance and Input Delay

In this paper, we address the H_∞ control problem of flexible spacecraft experiencing disturbance and time-varying input delay. First, we adopt the state-space method to develop a flexible spacecraft model with disturbance and time-varying input delay. Next, based on the Lyapunov stability theory and using the linear matrix inequality (LMI) method, we obtain an LMI delay-dependent H_∞ state feedback controller by constructing a new augmented Lyapunov function. The designed feedback controller gain depends on slack variable matrices rather than on the non-positive definite Lyapunov matrix. Finally, we use numerical simulations to verify the effectiveness of the proposed method and to analyze the delays, the H_∞ performance index, and the influence of delay-integral-inequality decomposition coefficients on the closed-loop system performance. Compared with traditional methods, the proposed method improves the flexibility of the controller design and reduces design conservatism by introducing slack variables matrices and the delay-integral-inequality decomposition coefficient.