Advanced Takagi‒Sugeno Fuzzy Systems

This monograph puts the reader in touch with a decade’s worth of new developments in the field of fuzzy control specifically those of the popular Takagi-Sugeno (T-S) type. New techniques for stabilizing control analysis and design based on multiple Lyapunov functions and linear matrix inequalities (LMIs), are proposed. All the results are illustrated with numerical examples and figures and a rich bibliography is provided for further investigation.

Control saturations are taken into account within the fuzzy model. The concept of positive invariance is used to obtain sufficient asymptotic stability conditions for the fuzzy system with constrained control inside a subset of the state space.

The authors also consider the non-negativity of the states. This is of practical importance in many chemical, physical and biological processes that involve quantities that have intrinsically constant and non-negative sign: concentration of substances, level of liquids, etc. Results forlinear systems are then extended to linear systems with delay. It is shown that LMI techniques can usually handle the new constraint of non-negativity of the states when care is taken to use an adequate Lyapunov function. From these foundations, the following further problems are also treated:

·        asymptotic stabilization of uncertain T-S fuzzy systems with time-varying delay, focusing on delay-dependent stabilization synthesis based on parallel distributed controller (PDC);

·        asymptotic stabilization of uncertain T-S fuzzy systems with multiple delays, focusing on delay-dependent stabilization synthesis based on PDC with results obtained under linear programming;

·        design of delay-independent, observer-based, H-infinity control for T–S fuzzy systems with time varying delay; and

·        asymptotic stabilization of 2-D T–S fuzzy systems.

Advanced Takagi–Sugeno Fuzzy Systems provides researchers and graduate students interested in fuzzy control systems with further approaches based LMI and LP.

• Delayed Systems
• Fuzzy Control
• Observer-based Fuzzy Control
• Positive Systems
• Reliable Control
• Saturated Control
• Takagi‒Sugeno Systems

“The monograph is of tangible value to all those who are interested in analysis and synthesis of control and stabilization algorithms realized for fuzzy rule-based models. The presentation of the material is clear, up-to-the point whereas the flow of the main ideas is coherent and logically organized. … All in all, the book could be a useful material to the readers engaged in the modem trends of control and fuzzy control, in particular.” (Witold Pedrycz, zbMATH 1323.93001, 2015)

• Department of Physics, University of Cadi Ayyad, Marrakech, Morocco

  Abdellah Benzaouia

• Laboratoire de Modélisation, Information et Systèmes, Université de Picardie Jules Verne, Amiens, France

  Ahmed El Hajjaji

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