This dissertation presents an extension of robust decentralized control design techniques for power systems, with special emphasis on design problems that can be expressed as minimizing a linear objective function under linear matrix inequality (LMI) in tandem with nonlinear matrix inequality (NMI) constraints. These types of robust decentralized control design problems are generally nonconvex optimizations, and are proven to be computationally challenging. Therefore, this dissertation proposes alternative computational schemes using: i) bordered-block diagonal (BBD) decomposition algorithm for designing LMI based robust decentralized static output feedback controllers, ii) sequential LMI programming method for designing robust decentralized dynamic output feedback controllers, and, iii) generalized parameter continuation method involving matrix inequalities for designing reduced-order decentralized dynamic output feedback controllers. First, this dissertation considers the problem of designing robust decentralized static output feedback controllers for power systems that guarantee connective stability despite the presence of uncertainties among the interconnected subsystems. The design problem is then solved using BBD decomposition algorithm that clusters the state, input and output structural information for the direct computation of the appropriate gain matrices. Moreover, the approach is flexible enough to allow the inclusion of additional design constraints such as the size of the gain matrices and the degree of robust stability while at the same time maximizing the tolerable upper bounds on the class of perturbations. Second, this research considers the problem of designing a robust decentralized fixed-order dynamic output feedback controller for power systems that is formulated as a nonconvex optimization problem involving LMIs coupled through bilinear matrix equation. In the design, the robust connective stability of the overall system is guaranteed while the upper bounds of the uncertainties arising from the interconnection of the subsystems as well as nonlinearities within each subsystem are maximized. The (sub)-optimal robust decentralized dynamic output feedback control design problem is then solved using sequential LMI programming method. Moreover, the local convergence property of this algorithm has shown the effectiveness of the proposed approach for designing (sub)-optimal robust decentralized dynamic output feedback controllers for power systems. Third, this dissertation considers the problem of designing a robust decentralized structure-constrained dynamic output feedback controller design for power systems using LMI-based optimization approach. The problem of designing a decentralized structure-constrained H2/Hinf controller is first reformulated as an extension of a static output feedback controller design problem for the extended system. The resulting nonconvex optimization problem which involves bilinear matrix inequalities (BMIs) is then solved using the sequentially LMI programming method. Finally, the research considers the problem of designing reduced-order decentralized Hinf controllers for power systems. Initially a fictitious centralized Hinf robust controller, which is typically high-order controller, is designed to guarantee the robust stability of the overall system against unstructured and norm bounded uncertainties. Then the problem of designing a reduced-order decentralized controller is reformulated as an embedded parameter continuation problem that homotopically deforms from the centralized controller to the decentralized controller as the continuation parameter monotonically varies. The design problem, which guarantees the same robustness condition of the centralized controller, is solved using a two-stage iterative matrix inequality optimization algorithm. Moreover, the approach is flexible enough to allow designing different combinations of reduced-order controllers between the different input/output channels. The effectiveness of these proposed approaches are demonstrated by designing realistic power system stabilizers (PSSs) for power system, notably so-called reduced-order robust PSSs that are linear and use minimum local-feedback information. Moreover, the nonlinear simulation results have confirmed the robustness of the system for all envisaged operating conditions and disturbances. The proposed approaches offer a practical tool for engineers, besides designing reduced-order PSSs, to re-tune PSS parameters for improving the dynamic performance of the overall system.