| This thesis focuses on absolute stability of Lur'e-Postnikov systems, with an emphasis on large-scale applications. The systems under consideration involve multiple nonlinearities, which are time-varying. New methods to establish absolute stability are formulated as convex optimization problems in the framework of Linear Matrix Inequalities (LMIs). When the system is unstable, design approaches of both state and output feedbacks are developed. The resulting feedback control law has two features: absolute stabilization and nonlinear sector maximization. The effectiveness of the design methods are demonstrated by two practical examples: the control of centrifugal governor and the synchronization of Chua's chaotic circuits.;For large-scale Lur'e-Postnikov systems, we pay particular attention to two issues: information structure constraints and computational complexity. To overcome the difficulties caused by these two issues, we design state feedbacks in three common-used control structures: decentralized control, overlapping control and Bordered Block Diagonal (BBD) control structure. The system is first decomposed into epsilon or BBD forms. Based on the decomposition result, the most suitable control structure is recognized. Finally, the state feedback of the selected control structure is designed by LMI approach.;When certain states are not available for control purpose, static output feedback is designed to establish absolute stability, and at the same time, maximize the nonlinear sector. In this thesis, we develop a design approach of static output feedback which can accommodate arbitrary information structure constraints. The proposed approach is also computationally efficient. The effectiveness of the proposed approach is demonstrated by a large-scale example. |
