标题： 基于圆锥扇区的线性参数变化系统分析与控制综合 显示英文标题

标题： Conic-sector-based analysis and control synthesis for linear parameter varying systems

摘要： 我们提出了一个关于线性参数变化（LPV）系统的圆锥扇区定理，在该定理中，对于某些参数值，传统的圆锥定义被违反。 我们表明，如果限制参数轨迹，使得系统以这些参数值运行的频率足够低，则可以将此类 LPV 系统定义为平均意义上的圆锥形式。 然后我们证明了这种平均意义上的圆锥定义在分析系统与具有适当圆锥特性的系统反馈连接时的稳定性是有用的。 这可以被视为经典圆锥扇区定理的扩展。 基于这个修改后的圆锥扇区定理，我们设计了圆锥控制器，允许闭环系统在非圆锥参数区域短暂运行。 由于这种额外的自由度，与传统设计相比，这些控制器导致的性能更不保守，传统设计中的控制器参数是根据包含植物动力学的最大圆锥来选择的。 我们通过演示证明了所提出的设计在稳定高渗透率可再生能源的电网的同时最小化功率传输损耗的有效性。 显示英文摘要

摘要： We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closed-loop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.