Stabilization and strong stabilization of lti systems by structured time-delay controllers

The main objective of this thesis is to develop controller design methods for stabilization and strong stabilization of linear time-invariant multi-input multi-output systems. In particular, the open-loop systems to be considered are allowed to be retarded or neutral time-delay systems which may have an arbitrary number of discrete time delays in the input/output channels or in the dynamics of the system itself. In order to stabilize such systems, an eigenvalue optimization-based controller design method is proposed in which the stabilization problem is formulated as the minimization of spectral abscissa function over the controller parameters. In this context, not only conventional finite-dimensional controllers but also time-delay controllers with an arbitrary number of artificial time delays are aimed to be designed. Furthermore, the controllers to be designed are allowed to be structured in an arbitrary form. A strong stabilization method is also developed as an extension of the stabilization method. More precisely, the centralized and/or decentralized strong stabilization problem is formulated by adding the controller stability as a constraint to the present stabilization problem. Finally, a new MATLAB-based software, which implements the analysis and controller design methods proposed in this thesis, is developed.