非线性奇异摄动系统的L_2增益干扰抑制

Interference Suppression for L_2 Gain in Nonlinear Singularly Perturbed Systems

将原系统分解为快慢两个子系统,并依据假设得到使快系统渐近收敛的状态反馈控制器.然后基于Lyapunov函数和逆推法构造出慢系统的状态反馈控制器,使得闭环系统对于所有有界干扰是内部稳定的,且从外部扰动输入到输出满足任意小的有界L2增益.通过求出第一个子系统的严格耗散不等式,递推得到全系统的严格耗散不等式,因此控制器设计过程避免了求解Hamilton-Jacobi方程,仿真实例说明了该方法的有效性和可行性.

Dividing a nonlinear singularly perturbed system into the fast and slow subsystems and according to the assumption, a state feedback controller with asymptotic convergence is obtained for the fast subsystem. Then, based on Lyapunov function and the backstepping design technique, a state feedback controller for the slow subsystem is also constructed, which enables the closed-loop system to be internally stable for all bounded interference and satisfies the arbitrarily small bounded L2 gain from exogeneous interference input to its output. The strictly dissipative inequality for the whole system can be deduced through recursive method after getting that for the first subsystem. So, the design process of controller can be done without the solution to Hamilton-Jacobi equation. A simulation example shows the feasibility and effectiveness of the approach proposed.