The use of linear matrix inequalities and Lyapunov functions is a powerful and commonplace tool for Takagi–Sugeno fuzzy controlled system analysis and synthesis. This paper shows how to split and handle the coupling terms arising from the existence of different input matrices in the subsystems. Then, a method is proposed which allows to synthesize, for a sufficient number of subsystems, the loc...

This paper is intended to propose a method to replace the original fuzzy linear system by two crisp linear systems. And then, the method is implemented by GMRES. If a fuzzy nonsingular linear system has a fuzzy solution, our method is able to obtain the solution. Otherwise, our method can only find a weak fuzzy solution. At last, some large scale numerical tests are presented.

Linear systems have important applications to many branches of Science and Engineering. In many applications, atleast some of the parameters of the system are represented by fuzzy rather than crisp numbers. This paper, discusses fully fuzzy linear systems with triangular fuzzy numbers. A matrix inversion method is proposed for solving Fully Fuzzy Linear System (FFLS) of equations. Finally, the ...

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

This paper studies the control of a pH process by using a neuro fuzzy controller with gain scheduling. As the process to be controlled is highly non-linear the PI-type fuzzy controller that will be used generally is not able to control the system adequately. For this, a very simple feedforward neural network trained on-line, is put at the output of the PI-type fuzzy controller in order to calcu...

Linear and Non-linear distortion influenced data transmission rate in communication system. In the presence of White Gaussian Noise linear distortion occurs in form of intersymbol interference (ISI) and co-channel interference (CCI). Amplifiers, modulator and demodulator subsystems are caused for Non-linear distortions along with nature of the medium. Different techniques are used to equalized ...

Research on control of non-linear systems over the years has produced many results: control based on linearization, global feedback linearization, non-linear H∞ control, sliding mode control, variable structure control, state dependent Riccati equation control, etc [5]. This chapter will focus on fuzzy control techniques. Fuzzy control systems have recently shown growing popularity in non-linea...

A highly nonlinear system controlled by a linear model predictive controller (MPC) may not exhibit a satisfactory dynamic performance. This has led to the development of a number of nonlinear MPC (NMPC) approaches that permit the use of first principles-based nonlinear models. Such models can be accurate over a wide range of operating conditions, but may be difficult to develop for many industr...

This paper presents the fuzzy linear control design method for a class of stochastic nonlinear time-delay systems with state feedback. First, the Takagi and Sugeno fuzzy linear model is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy linear controller is developed to stabilize the nonlinear system. The control law is obtained to ensure stochastical exp...

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H1 robustness performance. First, the Takagi and Sugeno fuzzy linear model is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performa...