Output Feedback Synthesis for Networked Control Systems With Packet Dropouts and Multiple Probability Sampling Periods: The Stochastic Communication Protocol Case

Communication imperfections, such as variable sampling periods and packet dropouts induced by insufficient network bandwidth, can degrade the control performance and even jeopardize the stability of networked control systems (NCSs). A stochastic communication protocol (SCP) is usually adopted to ensure that only one sensor node can transmit the output signal to the controller at each sampling instant, thus conserving network bandwidth resources. This article focuses on the output feedback synthesis problem for NCSs in the presence of the SCP, considering two-channel successive packet dropouts (SPDs) and multiple probability sampling periods (MPSPs). Among these, MPSPs mean that there are three or more different sampling rates in system. To address the output feedback synthesis problem, we first obtain the discrete-time augmented model of the closed-loop NCS with a dynamic output feedback controller. This model incorporates an equivalent sampling period representation between adjacent nonpacket-dropout instants, which plays a pivotal role in our analysis. Furthermore, a general analysis model is established by considering the effects of the SCP. Based on this model, conditions for designing the dynamic output feedback controller, represented by linear matrix inequalities (LMIs), are established using a two-step synthesis approach. In particular, the dimension of the obtained controller design conditions remains unchanged with respect to the upper bound of SPDs and the number of possible sampling periods, especially through the introduction of a matrix decomposition method, which is more general than existing results. Finally, the proposed method is demonstrated through an illustrated example.