Linear fuzzy controller: it is a linear nonfuzzy controller
Information Sciences: an International Journal
Fuzzy control theory: a nonlinear case
Automatica (Journal of IFAC)
Stability analysis and design of fuzzy control systems
Fuzzy Sets and Systems
Nonlinear feedback control systems: an operator theory approach
Nonlinear feedback control systems: an operator theory approach
On the analysis of fuzzy logic controllers
Fuzzy Sets and Systems
Towards a paradigm for fuzzy logic control
Automatica (Journal of IFAC)
A course in fuzzy systems and control
A course in fuzzy systems and control
Fuzzy controllers as gain scheduling approximators
Fuzzy Sets and Systems - Special issue on methods for data analysis in classificatin and control
Gain scheduling: from conventional to neuro-fuzzy
Automatica (Journal of IFAC)
Theory and application of a novel fuzzy PID controller using a simplifier Takagi-Sugeno rule scheme
Information Sciences: an International Journal - Special issue analytical theory of fuzzy control with applications
Industrial Applications of Fuzzy Logic and Intelligent Systems
Industrial Applications of Fuzzy Logic and Intelligent Systems
An approach to fuzzy control of nonlinear systems: stability and design issues
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control
IEEE Transactions on Fuzzy Systems
Logic-based switching controllers - A stepwise safe switching approach
Information Sciences: an International Journal
Stability analysis of the simplest Takagi-Sugeno fuzzy control system using circle criterion
Information Sciences: an International Journal
PI-Fuzzy controllers for integral plants to ensure robust stability
Information Sciences: an International Journal
On controllability and observability of fuzzy dynamical matrix Lyapunov systems
Advances in Fuzzy Systems - Regular issue
Design and optimization of membership function based on analytical structure and immune algorithm
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 6
Robust Fuzzy Control of Electrical Manipulators
Journal of Intelligent and Robotic Systems
Survey paper: A survey on industrial applications of fuzzy control
Computers in Industry
On the accessibility/controllability of fuzzy control systems
Information Sciences: an International Journal
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In the first part of this paper, we investigate explicit structure of the typical Takagi-Sugeno (TS) fuzzy PI and PD controllers. By typical, we mean the use of at least three trapezoidal or triangular input fuzzy sets for each input variable, fuzzy rules with linear consequent, Zadeh fuzzy logic AND operator and the centroid defuzzifier. This configuration covers many TS fuzzy controllers in the literature. We mathematically prove these fuzzy controllers to be nonlinear PI (or PD) controllers with proportional-gain and integral-gain (or derivative-gain) changing with output of the controlled system. We reveal these fuzzy controllers to be inherently nonlinear gain scheduling PI (or PD) controllers with different variable gains in different regions of input space. The gains constantly change even in the same region, and switch continuously and smoothly between adjacent regions. The explicit structural expressions of the fuzzy controllers are derived and their characteristics, including the bounds and geometrical shape of the gain variation, are studied. In the second part of the paper, we apply the Small Gain Theorem to the derived structures of the fuzzy controllers and establish a sufficient global BIBO stability criterion for nonlinear systems controlled by the fuzzy controllers. Local stability is also examined.