不确定系统D稳定的鲁棒H_∞可靠性控制

H_∞ Reliable Control of Uncertain Systems with D-stability Constraints

研究了一类不确定系统区域稳定的鲁棒H∞可靠性控制器的设计方法,其目的是通过设计状态反馈控制器,使闭环系统的极点被配置在给定的圆盘中,同时,当有外生扰动,以及所有可能的不确定及其敏感执行器失灵的时候,依然能满足闭环传递函数的H∞范数有界的约束。借助于广义的Riccati矩阵不等式,给出了控制器存在的充分条件,同时给出了所期望控制器的解析式。最后,通过一个仿真例子,说明该方法的可行性。

The problem of robust H∞ controller design for a class of uncertain systems with D-stability constraints was studied. The design of a state feedback controller was proposed that guarantees the closed-loop poles placed within a specified disk and an H∞ -norm bounded constraint on attenuation disturbances, including failure signals, for all admissible uncertainties as well as actuator failures. By virtue of the modified Riccati matrix inequality, the sufficient condition for existence of desired controller was obtained. Meanwhile, the analytical expression of the set of desired controllers was proposed. An illustrative example is provided to demonstrate the applicability of the proposed method.