  This paper studies the tracking control problem of nonlinear networked and
quantized control systems (NQCSs) with communication delays. The desired
trajectory is generated by a reference system. 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 like time-varying transmission intervals, time-varying transmission
delays, packet dropouts, scheduling and quantization effects, which lead to
non-vanishing network-induced errors and affect the tracking performances. As a
result, we develop a general hybrid system model for NQCSs with all
aforementioned issues. Based on the Lyapunov approach, sufficient conditions
are established to guarantee the stability of the tracking error with respect
to the non-vanishing 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 (e.g., Round-Robin protocol and Try-Once-Discard protocol) and
quantizers (e.g., zoom quantizer and box quantizer), Lyapunov functions are
constructed explicitly. Finally, a numerical example is presented to
demonstrate the developed theory.
