Tracking Control of Nonlinear Networked and Quantized Control Systems With Communication Delays

This note studies the tracking control problem of nonlinear networked and quantized control systems (NQCSs) with communication delays. The communication network is to guarantee the information transmission among the plant, the reference system, and the controller. The communication network also brings about some undesired issues, which lead to nonvanishing network-induced errors and affect the tracking performance. As a result, we first develop a hybrid system model for NQCSs under the network-induced issues. Based on the Lyapunov approach, sufficient conditions are established to guarantee the tracking performance with respect to the nonvanishing network-induced errors. The obtained conditions lead to a tradeoff between the maximally allowable transmission interval and the maximally allowable delay. Furthermore, the existence of Lyapunov functions satisfying the obtained conditions is studied. For specific time-scheduling protocols and quantizers, Lyapunov functions are constructed explicitly. Finally, a numerical example is presented to demonstrate the developed theory.