Stability and performance of control systems with limited feedback information

This thesis studies linear control systems with limited feedback information. The focus is on two types of limitations on the feedback information, dropout and quantization. By dropout, we mean that the desired feedback measurement is missed. By quantization, we mean the feedback measurement is described by a finite number of bits, which introduces ``measurement error'. This thesis analyzes the effect of dropout and quantization on stability and performance of control systems and develops synthesis methods that improve system performance in the face of such limited information. We consider two dropout models, independent and identically distributed (i.i.d.) processes and Markov chains. For a control system with i.i.d. dropouts, we provide a necessary and sufficient stability condition and a closed-form expression for the output's power spectral density (PSD). Based on this PSD result, we identify an equivalent linear time-invariant (LTI) system which can be used to do synthesis. As an example, we design the optimal dropout compensator. For a control system with dropouts governed by a Markov chain, we provide a necessary and sufficient stability condition and a method to compute performance measured by the output's power. Based on the performance result, we propose a method to design the optimal dropout policy which minimizes the degradation of system performance under the given dropout rate constraint. We extend the performance results on Markovian dropouts to distributed control systems. For a quantized control system, we derive the minimum constant bit rate to guarantee stability. A dynamic bit assignment policy (DBAP) is proposed to achieve such minimum bit rate. We also study the performance of quantized systems. For a noise-free quantized system, we prove that DBAP is the optimal quantization policy with performance measured by the L-2 norm of the quantization error. For a quantized system with bounded noise, performance is measured by the ultimate upper bound of quantization error. We present both a lower bound and an upper bound on the optimal performance for quantized systems with bounded noise. The upper bound can always be achieved by the proposed DBAP. So DBAP is at least a sub-optimal quantization policy with the known performance gap.