This paper deals with an application of robust state feedback pole placement for discrete-time polytopic systems with stochastic disturbance attenuation. A set of stochastic signals is described using differential entropy functional. In the paper the parameter-independent robust state-feedback controller design procedure for linear discrete-time polytopic systems with theoretic-information constraints on the set of external random disturbances is proposed. Such additional constraints allow to find a tradeoff between ${\mathcal{H}}_2$ and ${\mathcal{H}}_{\infty }$ control with better control energy consumption and improved robustness against random disturbances. This approach is applied to PWM inverters with LCL filters connected to the grid under uncertain parameters. Simulation results indicates that proposed controller allows to improve frequency and transient responses with better performance than existing ones.

本文处理具有随机干扰衰减的离散时间多面体系统的鲁棒状态反馈极点放置的应用。使用微分熵泛函描述一组随机信号。本文提出了对外部随机扰动集具有理论信息约束的线性离散时间多面体系统的参数无关鲁棒状态反馈控制器设计程序。这种额外的约束允许在${\mathcal{H}}_2$ 和 ${\mathcal{H}}_{\infty }$ 控制具有更好的控制能量消耗和提高对随机干扰的鲁棒性。这种方法适用于在不确定参数下连接到电网的 LCL 滤波器的 PWM 逆变器。仿真结果表明，所提出的控制器允许以比现有控制器更好的性能改善频率和瞬态响应。