This paper is concerned with the ${\ell }_2$–${\ell }_{\mathrm{\infty }}$ output-feedback control problem for a class of two-dimensional (2-D) switched systems described by the general Fornasini–Marchesini second model under the stochastic communication protocol (SCP). In a networked 2-D switched control system, the sensors and the controller are typically connected through a shared communication network of limited bandwidth, which is likely to result in data collision problem. To circumvent this network-induced problem, a new SCP is dedicatedly put forward for the 2-D switched system in order to orchestrate the transmission order of sensor nodes, under which only one sensor node obtains the privilege to access the network at each transmission instant. Then, based on the nominal system information compensation, a set of new mode-dependent output-feedback controllers is designed for 2-D switched systems subject to SCP and external disturbances. Moreover, using the average dwell-time approach, sufficient conditions are established to ensure the existence of the desired controllers that guarantee both the exponential mean-square stability and the ${\ell }_2$–${\ell }_{\mathrm{\infty }}$ performance. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed controller design method.

这篇论文是关于 ${\ell }_2$——${\ell }_{\mathrm{\infty }}$在随机通信协议 (SCP) 下，由通用 Fornasini-Marchesini 第二模型描述的一类二维 (2-D) 交换系统的输出反馈控制问题。在联网的二维切换控制系统中，传感器和控制器通常通过带宽有限的共享通信网络连接，这很可能导致数据冲突问题。为了规避这个网络引起的问题，专门为二维交换系统提出了一种新的SCP来编排传感器节点的传输顺序，在这种情况下，在每个传输时刻只有一个传感器节点获得访问网络的权限. 然后，基于标称系统信息补偿，一组新的依赖于模式的输出反馈控制器设计用于受 SCP 和外部干扰影响的二维开关系统。此外，使用平均停留时间方法，建立了充分的条件来确保所需控制器的存在，以保证指数均方稳定性和${\ell }_2$——${\ell }_{\mathrm{\infty }}$表现。最后，给出了一个数值例子来证明所提出的控制器设计方法的有效性。