sensor resolution impact on dynamics

Is there a way to apply sensor model inside dynamics of a system in Matlab?

Suppose dynamics of open loop system are:

xdot = A x + B u
y = c x + D u

x is 4 states (th1, th2, th1_dot, th2_dot). The open loop system is denoted by G_p, and the control is denoted by G_c. The closed loop system would be

G_cl = Gp Gc/(1+Gp*Gc)

For now, I model sensor with floor function in Matlab and after controlling the system and simulating the response of system to a given input, I quantize one of the states with floor function. But, since this does not give realistic impact of sensor on other states, I want to move sensor model inside my open loop dynamics or at least before the controller is implemented.

I appreciate any ideas.