Design of Sliding Mode Control Subject to Packet Losses

This technical note investigates the design of sliding mode control subject to packet losses. It is assumed that there exists a communication network in the feedback loop, and the dropout of data packet may occur. First, an estimation method is proposed to compensate the packet dropout. Subsequently, a discrete-time integral sliding surface involving dropout probability is introduced and a sliding mode controller is designed. By using the stochastic Lyapunov method, the state trajectories are shown to enter into (in mean square) a neighborhood of the specified sliding surface. Meanwhile, the stability of sliding mode dynamics is also ensured. Finally, numerical simulation example is provided.