Two-dimensional Systems ― From Introduction to State of the Art

A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The problems of delay and saturation are treated at the same time. The authors obtain novel results on continuous 2-D systems using the unidirectional Lyapunov function. The control synthesis and the saturation and delay conditions are presented as linear matrix inequalities. Illustrative examples are worked through to show the effectiveness of the approach and many comparisons are made with existing results.

The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems. Solutions for the filter-design problems are demonstrated by computer simulation. The text builds up to the development of state feedback control for 2-D Takagi–Sugeno systems with stochastic perturbation. Conservatism is reduced by using slack matrices and the coupling between the Lyapunov matrix and the system matrices is broken by using basis-dependent Lyapunov functions. Mean-square asymptotic stability and prescribed H-infinity performance are guaranteed.

Two-Dimensional Systems emphasizes practical approaches to control and filter design under constraints that appear in real problems and uses off-the-shelf software to achieve its results. Researchers interested in control and filter design for multidimensional systems, especially multi-dimensional fuzzy systems, will find this book a useful resource as will graduate students specializing in dynamical sytems.

Abdellah Benzaouia was born in Attaouia (Marrakech) in 1954. He received the degree of Electrical Engineering at the Mohammedia school (Rabat) in 1979 and the Doctorat (PhD) at the University Cadi Ayyad in 1988. He is actually professor at the University of Cadi Ayyad (Marrakech) where he is also head of the laboratory of research LAEPT, CNRST laboratory. His research interests are mainly constrained control, robust control, pole assignment, systems with Markovian jumping parameters, hybrid systems and fuzzy systems. He collaborates with many teams in France, Canada, Spain and Italy.
Abdelaziz Hmamed was born in Sefrou, Morocco, in 1951. He received his Doctorate of State degree in Electrical Engineering from the Faculty of Sciences, Rabat, Morocco, in 1985. Since 1986, he has been with the Department of Physics, Faculty of Sciences, Dhar El Mehraz at Fes, where he is currently a Full Professor. His research interests are delay systems, stability theory, systems with constraints, 2-d systems and applications.
Fernando Tadeo is Professor of the School of Engineering at the University of Valladolid. He graduated from the same university, in Physics in 1992, and in Electronic Engineering in 1994. After completing an M.Sc. in Control Engineering in the University of Bradford, U.K., he went back to Valladolid, where he got his Ph.D. degree. His main interest area is Feedback Systems with Constraints, in particular Positive Systems, collaborating with teams in Morocco, Tunisia, France and Germany. This research is focused on applications in Process Control (Desalination and Electrolyzation Processes) and Renewable Energies (Wind, Solar and Salinity Gradient).