On the effect of quantization on performance at high rates

We study the effect of quantization on the performance of a scalar dynamical system in the high rate regime. We evaluate the LQ cost for two commonly used quantizers: uniform and logarithmic and provide a lower bound on performance of any centroid-based quantizer based on entropy arguments. We also consider the case when the channel drops data packets stochastically

Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System

Minimal data rate stabilization of nonlinear systems over networks with large delays

Control systems over networks with a finite data rate can be conveniently modeled as hybrid (impulsive) systems. For the class of nonlinear systems in feedfoward form, we design a hybrid controller which guarantees stability, in spite of the measurement noise due to the quantization, and of an arbitrarily large delay which affects the communication channel. The rate at which feedback packets are transmitted from the sensors to the actuators is shown to be arbitrarily close to the infimal one.Comment: 16 pages; references have now been adde