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...

In this paper , some results about the index of matrix and Drazin inverse are given. We then explain applications of them in solving singular linear system of equations.

This paper investigates the problem of state feedback H∞ control for singular systems through delta operator approach. Firstly, a bounded real lemma corresponding to a singular continuous system under the framework of the delta operator model is obtained. Then, the existence condition and explicit expression of a desirable H∞ controller for the singular delta operator system are presented. As s...

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...

Many linear macroeconomic models can be cast in the …rst-order form, AEtyt+1 = Byt +CEtxt; if the matrix A is permitted to be singular. For this singular linear di¤erence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinental polynomial jAz ¡ Bj is not zero for some value of z, and (ii) a rank condition is satis…ed which is a ...

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...

in this paper, a new t-s fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. fuzzy controller is designed based on the parallel distributed compensation (pdc), and with a new lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...

This paper addresses the problem of designing an H∞ filter for a class of nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a fuzzy H∞ filter that guarantees the L2-gain from an exogenous input to a filter error to be less than or equal to a prescribed value. In order to alleviate the ill-conditio...