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Horacio Marquez

Professor

Engineering

Electrical and Computer Engineering

About Me

Horacio J. Marquez received his BSc degree from the Instituto Tecnologico de Buenos Aires (Argentina), and his MSc, MEng, and PhD degrees in electrical engineering from the University of New Brunswick, Fredericton, Canada, in 1987, 1990 and 1993, respectively.


From 1993 to 1996 he held visiting appointments at the Royal Roads Military College, and the University of Victoria, Victoria, British Columbia. Since 1996 he has been with the Department of Electrical and Computer Engineering at the U of A, where he is currently a Professor. In 2008 he was a guest research professor at Nancy University – University Henri Poincare, France.


Dr. Marquez is a Fellow of IET (formerly IEE) and is currently an Area Editor for the International Journal of Robust and Nonlinear Control. He is the Author of “Nonlinear Control Systems: Analysis and Design” (Wiley, 2003). He is the recipient of the 2003-2004 McCalla Research Professorship awarded by the University of Alberta. His current research interests include nonlinear dynamical systems and control, nonlinear observer design, robust control, and applications.


Research

Research Interests

My interests are in the area of nonlinear control theory, with emphasis on stability theory and robust and optimal control. Robust control is the branch of control theory that takes explicit account of the fact that the mathematical models used in control design are never perfect. This is widely recognized as a very important problem. Indeed, due to the existence of model uncertainties, controllers which operate very well in computer simulations often fail to provide adequate performance when put to work with the actual plant. For linear time-invariant systems, robust control has reached certain degree of maturity. My long term interest is in the formulation of a comprehensive theory of robust control for nonlinear systems, which can deal with complex industrial systems.


Current Research

Over the past year my work focused on three problems: sampled-data control, nonlinear observers, and, chaos control and synchronization.


Sampled data nonlinear control is a relatively new area that takes account of the fact that exact discrete-time models of continuous-time plants cannot be obtained due to the lack of existence of closed form solutions of nonlinear differential equations. For the past three years we have been working on the development of a theory of multirate sampled-data control. We were able to show that multirate systems can significantly improve the performance of single rate controllers. We are currently working on the formulation of a design technique for multirate nonlinear controllers.


Work on nonlinear observers focused on the use of a new observer structure, which I recently introduced. In cooperation with my graduate students, we have developed a complete observer design procedure for Lipschitz systems along with extensions to discrete-time and multirate systems. Currently our work is focused on an extension of previous results to a larger class of systems known as "one-sided Lipschitz."


Nonlinear dynamical systems can have very interesting properties. One of those properties is called "chaos". Chaos is characterized by critical dependence on initial conditions. My work in this area focuses on how to synchronize the trajectories of two identical dynamical systems. If successful, chaotic systems can be used to send communication message through a secure channel.