Stability analysis and design of fuzzy control systems
Fuzzy Sets and Systems
An introduction to fuzzy control
An introduction to fuzzy control
Theoretical aspects of fuzzy control
Theoretical aspects of fuzzy control
A course in fuzzy systems and control
A course in fuzzy systems and control
Robust stability analysis of fuzzy control systems
Fuzzy Sets and Systems
L2-stabilization design for fuzzy control systems
Fuzzy Sets and Systems
Nonlinear Control Systems II
Hyperstability of Control Systems
Hyperstability of Control Systems
Stability Issues in Fuzzy Control
Stability Issues in Fuzzy Control
Semiglobal stabilization of nonlinear systems using fuzzy control and singular perturbation methods
Fuzzy Sets and Systems - Control and applications
Stable and optimal adaptive fuzzy control of complex systems using fuzzy dynamic model
Fuzzy Sets and Systems - Theme: Fuzzy control
Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties
Fuzzy Sets and Systems - Modeling and control
Stable adaptive control of fuzzy dynamic systems
Fuzzy Sets and Systems - Modeling and control
Fuzzy Modeling and Control
Stability and stabilizability of fuzzy-neural-linear control systems
IEEE Transactions on Fuzzy Systems
An approach to fuzzy control of nonlinear systems: stability and design issues
IEEE Transactions on Fuzzy Systems
New design and stability analysis of fuzzy proportional-derivative control systems
IEEE Transactions on Fuzzy Systems
A new methodology to improve interpretability in neuro-fuzzy TSK models
Applied Soft Computing
A general and formal methodology to design stable nonlinear fuzzy control systems
IEEE Transactions on Fuzzy Systems
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The stability of nonlinear systems has to be investigated without making linear approaches. In order to do this, there are several techniques based on Lyapunov's second method. For example, Krasovskii's method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems. This method requires the calculation of the Jacobian matrix. In this paper, an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed. Later, this model is used to compute the Jacobian matrix of a closed loop fuzzy system. Next, an algorithm to solve the Jacobian matrix is proposed. The algorithm uses a methodology based on the extension of the state vector. The developed algorithm is completely general: it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models, and it allows the compound of different membership functions in a same model. We have developed a MATLAB's function that implements the improved algorithm, together with a series of additional applications for its use. The designed software provides complementary functions to facilitate the reading and writing of fuzzy systems, as well as an interface that makes possible the use of all the developed functions from the MATLAB's environment, which allows to complement and to extend the possibilities of the MATLAB's Fuzzy Logic Toolbox. An example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented. The work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems.