Communication-Delay-Distribution-Dependent Networked Control for a Class of T–S Fuzzy Systems

This paper investigates a robust networked control for a class of Takagi-Sugeno (T-S) fuzzy systems. The controller design specifically takes probabilistic interval distribution of the communication delay into account. A general framework of networked control is first proposed. The two main features are 1) the zero-order hold can choose the latest control input signal when the packets received are out-of-order, and 2) as the result of 1), the models of the all kinds of uncertainties in networked signal transfer-including network-induced delay and data packet dropout-are under a unified framework. Next, if the probability distribution of communication delay is known or specified in a design process, sufficient stability conditions for networked T-S fuzzy systems are derived, which are based on the Lyapunov theory. Following this, a stabilizing controller design method is developed, which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well. Finally, a numerical example is used to show the application of the theoretical results obtained in this paper.