This book studies 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 only described by a finite number of bits, which introduces ``measurement error''. We consider two dropout models, independent and identically distributed (i.i.d.) processes and Markov chains. Under i.i.d. dropouts, we provide a closed-form expression for the output's power spectral density, which can be used to greatly simplify system synthesis, such as design of the optimal dropout compensation. Under dropouts governed by a Markov chain, we provide a necessary and sufficient stability condition, and propose a method to compute performance measured by the output's power. For a quantized system, we derive the minimum constant bit rate to guarantee stability and propose a dynamic bit assignment policy(DBAP) to achieve such minimum bit rate. It also investigates the system performance under DBAP. The preliminary research confirms the superiority of DBAP against other quantization policies.

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