This book focuses on filtering, control and model-reduction problems for two-dimensional (2-D) systems with imperfect information. The time-delayed 2-D systems covered have system parameters subject to uncertain, stochastic and parameter-varying changes. After an initial introduction of 2-D systems and the ideas of linear repetitive processes, the text is divided into two parts detailing: · General theory and methods of analysis and optimal synthesis for 2-D systems; and · Application of the general theory to the particular case of differential/discrete linear repetitive processes. The methods developed provide a framework for stability and performance analysis, optimal and robust controller and filter design and model approximation for the systems considered. Solutions to the design problems are couched in terms of linear matrix inequalities. For readers interested in the state of the art in linear filtering, control and model reduction, Filtering and Control for Classes of Two-Dimensional Systems will be a useful reference for exploring the field of 2-D systems either from a purely theoretical research perspective or from the point of view of a multitude of potential applications including image processing, and the study of seismographic data or thermal processes.