微分フラットシステムに対するL₂規範に基づく安定化ゲイン設計法

抄録

We consider input-to-state-stability gain (ISS-gain) design for a differentially flat system disturbed by bounded noise. Firstly, we design a C^∞ differential strict control Lyapunov function (CLF) for the augmented linear system on the extended state space. The CLF satisfies predetermined L₂ norms performance by solving state feedback H_∞ control problems to attenuate persistent disturbance levels. Then, an Input-state-stability CLF (ISS-CLF) is derived from the CLF by applying a dynamic extension method and a minimum projection method. The ISS-CLF and the predetermined L₂ norms performance give the analytic ISS gain function. Finally, we specify the L₂ norms performance bounds of the disturbance attenuation controller for the differentially flat system. The effectiveness of the proposed method is confirmed by computer simulation of marine vessel control.