Dissipative PID control for uncertain positive Roesser system under the try-once-discard protocol

Abstract

This paper addresses the problem of dissipative proportional–integral–derivative (PID) control for the delayed positive Roesser system with interval uncertainties under the try-once-discard (TOD) protocol. To alleviate the undesired data congestion phenomenon in the shared communication network, the TOD protocol is introduced to regulate which sensor node could release its measurement at each transmission instant. An output-feedback-based PID controller is designed for the two-dimensional (2-D) system with TOD protocol. Based on the co-positive Lyapunov–Krasovskii function method, sufficient criteria in the linear programming form are attained to ensure the positivity, 2-D (ζ,η)-γ-dissipativity and robust asymptotic stability of the closed-loop system. Finally, an illustrative example is given to show effectiveness of the PID control scheme designed.