Dual-channel event-triggered control for positive nonlinear systems

This paper focuses on the problem of dual-channel event-triggered control for positive nonlinear systems. A dual-channel event-triggered transmission scheme is proposed to determine whether the data packets should be released or not. Two 1-norm-based event-trigger conditions are designed for the sensor-controller channel and controller-actuator channel, respectively. The condition of the system remaining positivity with the designed event-trigger conditions and feedback control law is provided. By using the Lyapunov method and matrix decomposition technique, a sufficient criterion ensuring the closed loop system to be asymptotically stable is proposed. For the linearisation purpose, the control gain is delicately decomposed into a nonnegative component and a non-positive component. Zeno behaviour of the designed event-triggered transmission of sampled data packets is further rigorously proved to be excluded. An example of water pollution control system is provided to show the effectiveness of the obtained results.