Practical second order sliding modes in single-loop networked control of nonlinear systems

This paper presents a novel Second Order Sliding Mode (SOSM) control algorithm for a class of nonlinear systems subject to matched uncertainties. By virtue of its Event-Triggered nature, it can be used as a basis to construct robust networked control schemes. The algorithm objective is to reduce as much as possible the number of data transmissions over the network, in order not to incur in problems typically due to the network congestion such as packet loss, jitter and delays, while guaranteeing satisfactory performance in terms of stability and robustness. The proposed Event-Triggered SOSM control strategy is theoretically analysed in the paper, showing its capability of enforcing the robust ultimately boundedness of the sliding variable and its first time derivative. As a consequence, it is also possible to prove the practical stability of the considered system, in spite of the reduction of transmissions with respect to a conventional SOSM control approach. Moreover, in order to guarantee the avoidance of the notorious Zeno behaviour, a lower bound for the time elapsed between two consecutive triggering events is provided.