In this paper, dwell time method incorporated with multiple Lyapunov-like functions are utilized to investigate the finite-region asynchronously switched control problems for 2-D switched system in the Fornasini-Marchesini local state-space (FMLSS) model. The finite-region stability (FRS) conditions for 2-D asynchronously switched FMLSS model are attained when there is no external disturbances. Then, the sufficient conditions in terms of dwell time scheme for the finite-region H_∞ control of 2-D asynchronously switched FMLSS model are derived. Based on the established conditions, the sufficient solvability conditions for designing the corresponding finite-region mode-dependent state feedback controllers are given according to linear matrix inequalities (LMIs). Two numerical examples are employed to show the effectiveness of the provided design methods.

在本文中，结合多个Lyapunov类函数的驻留时间方法被用于研究Fornasini-Marchesini局部状态空间（FMLSS）模型中二维切换系统的有限区域异步切换控制问题。在没有外部干扰的情况下，可以获得二维异步切换FMLSS模型的有限区域稳定性（FRS）条件。然后，在用于有限区域的停留时间方案方面的充分条件ħ _∞推导了二维异步切换FMLSS模型的控制。根据建立的条件，根据线性矩阵不等式（LMI）给出了设计相应的有限区域模式相关状态反馈控制器的充分可解条件。使用两个数值示例来说明所提供设计方法的有效性。