This article is concerned with the design and performance optimization of feedback controllers for state‐based switching bilinear systems (SBLSs), where subsystems take the form of bilinear systems in different state space polyhedra. First, by further dividing the subregions into smaller regions and designing region‐dependent feedback controllers in the resulting regions, the SBLSs can be transformed into corresponding switching linear systems (SLSs). Then, for these SLSs, by imposing contractility conditions on the Lyapunov functions, an upper bound on the infinite horizon quadratic cost can be obtained. Optimizing this upper bound yields the controller design. The optimization problem is formulated as a linear matrix inequalities optimization problem, which can be solved efficiently. Finally, the stability of the close‐loop system under the proposed controller is established step by step through a decreasing overall Lyapunov function.

中文翻译：

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为基于状态的开关双线性系统优化反馈控制器的性能

本文关注基于状态的开关双线性系统（SBLS）的反馈控制器的设计和性能优化，其中子系统在不同状态空间多面体中采用双线性系统的形式。首先，通过将子区域进一步划分为较小的区域，并在结果区域中设计区域相关的反馈控制器，可以将SBLS转换为相应的开关线性系统（SLS）。然后，对于这些SLS，通过在Lyapunov函数上施加可收缩性条件，可以获得无限地平线二次成本的上限。优化此上限将产生控制器设计。将优化问题表述为线性矩阵不等式优化问题，可以有效地解决该问题。最后，