  This paper studies the resilient control of networked systems in the presence
of cyber attacks. In particular, we consider the state feedback stabilization
problem for nonlinear systems when the state measurement is sent to the
controller via a communication channel that only has a finite transmitting rate
and is moreover subject to cyber attacks in the form of Denial-of-Service
(DoS). We use a dynamic quantization method to update the quantization range of
the encoder/decoder and characterize the number of bits for quantization needed
to stabilize the system under a given level of DoS attacks in terms of duration
and frequency. Our theoretical result shows that under DoS attacks, the
required data bits to stabilize nonlinear systems by state feedback control are
larger than those without DoS since the communication interruption induced by
DoS makes the quantization uncertainty expand more between two successful
transmissions. Even so, in the simulation, we show that the actual quantization
bits can be much smaller than the theoretical value.
