Effects of measurement quantization in the feedback loop of discrete-time linear control systems

In this thesis we investigate the effects of quantization in the feedback loop of linear control systems. Our concentration is twofold; first we study the dynamics of the system operating in the presence of quantization and second we address the problem of enhancing our knowledge of the current system states by employing information gathering techniques. We increase our information about the current state values using a recursive computation that uses the record of the quantized readings.;We model the quantization as a deterministic and memoryless nonlinearity. This allows us to describe the evolution of the system by iterating a nonlinear mapping. We can then use techniques from the ergodic theory of dynamical systems to study the dynamics of the system.;We demonstrate that systems which would have a unique globally asymptotically stable equilibrium without quantization can exhibit multiple equilibria, limit cycles or chaotic motion with quantization present. We produce some results that specify which types of behaviors will be observed over various parameter ranges. Furthermore we calculate the locations of the equilibria and the points on the periodic orbits. In the case of chaotic motion we describe its statistical properties by computing an invariant density for the nonlinear mapping that describes the closed-loop system.;While our results on the dynamics are descriptive in nature, our information gathering techniques are prescriptive. We demonstrate that by careful use of the feedback control, we can develop information gathering control strategies that enable us asymptotically to gain more information about the current state of the system than is readily available from the quantized measurements. We show that in some cases we can increase the extent of our knowledge arbitrarily and calculate an upper bound on asymptotically available current state information for other cases.