Saturated Control of Linear Systems

This book deals with a combination of two main problems for the first time. They are saturation on control and on the rate (or increment) of the control, and the solution of unsymmetrical saturation on the control by LMIs. It treats linear systems in state space form, in both the continuous- and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate, such that the system evolves respecting incremental or rate constraints if any. A pole assignment technique is then used to solve the problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on control alone or on both control and its increment or rate. Illustrative examples show the application of these methods on academic examples or on such real plant models as the double integrator system. This problem is then extended to various others including:

• systems with constraints and perturbations;
• singular systems with constrained control;
• systems with unsymmetrical saturations;
• saturated systems with delay, and
• 2-D systems with saturations.

The solutions obtained are of two types:

• necessary and sufficient conditions solved with linear programming techniques; and
• sufficient conditions under LMIs.

A new approach extends existing techniques for dealing with symmetrical saturations to take direct account of unsymmetrical saturations into account with LMIs. This tool enables the authors to obtain new results on continuous- and discrete-time systems. The book uses illustrative examples and figures and provides many comparisons with existing results.

Systems theoreticians interested in multidimensional systems and practitioners working with saturated and constrained controllers will find the research and background presented in Saturated Control of Linear Systems to be of considerable interest in helping them overcome problems with their plant and in stimulating further research.

Abdellah Benzaouia received the degree of Electrical Engineering at the Mohammedia School (Rabat) in 1979 and his PhD at the University Cadi Ayyad in 1988. Presently, he is a 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. Professor Benzaouia has about 1500 citations according to Researsh Gate. He has also published 3 books on saturated switching, saturated T–S fuzzy and saturated 2-dimensional systems.

Fouad Mesquine received the Master’s and PhD degrees from Cadi Ayyad University Marrakech, Morocco in 1992 and 1997, respectively both in automatic control. He is currently a member of and professor in the physics department of the Faculty of Sciences, Marrakech, Morocco. Professor Mesquine has about 500 citations according to Researsh Gate. His main research interests are: constrained control, robust control, time-delay systems control, pole assignment in complex plane regions, 2-dimensional systems, fractional systems.

Mohamed Benhayoun received a 3rd cycle PhD. in electrical engineering and instrumentation at the University Paris VI, Pierre and Marie Curie, in 1985. He received the Ph.D. in automatic control at the University Cadi Ayyad Marrakesh in 2011. Between 1985 and 1987, he joined the Higher National School of Marrakech. Since 1987 he has occupied a full position at the Faculty of Sciences Semlalia of the Cadi Ayyad University of Marrakech. During this time, Professor Benhayoun was interested to several subjects of physics and especially in the field of electrical engineering such as electronics, signal processing and automatic control as two-dimensional systems, fractional systems and saturated systems.