Simultaneous stabilization of linear systems is a fundamental issue in system and control theory, and is of theoretical significance as well as practical interest. Some open problems have been proposed in the literature as indications of the potential complexity of simultaneous stabilization questions. These problems are simply-stated but are very hard to solve. The system and control community will benefit from the resolutions to these difficult problems. The first part of this dissertation is devoted to these open problems. Firstly, the well-known “Generalized Champagne Problem” on simultaneous stabilization of linear systems is solved by using complex analysis and Blondel's technique. Based on the recent advances in automated inequality-type theorem proving, a novel stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature. Secondly, for “Chocolate Problem” and “Whisky Problem”, the underlying analysis leads to some theoretical results. Some conditions on the nonexistence of the stabilizing controller for the specified “Chocolate Problem'' and some conditions on the existence of a certain type of stabilizing controllers for “Whisky Problem'' are presented. Meanwhile, some prospects on the further investigation to these open problems of simultaneous stabilization are given. In the second portion of this dissertation, network planning in RFID (Radio Frequency Identification) systems is considered. According to some features which RFID systems share with other wireless communication systems and some particularities which only show in RFID systems, a discrete model on the network planning in RFID systems is established. Finally, some combinational optimization procedures for network planning in RFID systems are presented, which originate from tabu search and genetic algorithm respectively.