In this paper, the concept of stability for fuzzy control systems is discussed from a mathematical point of view. Our main objective is to investigate the stability of fuzzy Linear systems with bounded input and bounded output. Necessary and sufficient conditions for this kind of stability are presented by a theorem and it is illustrated by solving an example.

In this paper, we show the stability of Gustafson, Wei-dmann, Kato, Wolf, Schechter and Browder essential spectrum of bounded Linear operators on Banach spaces which remain invari-ant under additive perturbations belonging to a broad classes of operators U such that g(Um)<1 where g(.) is a measure of non-compactness.

In this research, the effects of variation of physical transport coefficient of fluid, such as kinematic viscosity and thermal diffusivity coefficient, on the primary instability of natural convection has been investigated. Accordingly, the governing equations are calculated for the onset of free convective flow by using the perturbation theory on the variation of temperature and velocity. Using the theory of Linear stability and the wave function, it can be defined the minimum Rayleigh number as critical Rayleigh number in assumed eigenvalue problem. It is assumed that the flow variables, such as the thermal diffusivity coefficient and kinematic viscosity, change exponentially relative to the location. The simulation results show that the critical-wave number function is a even function. Also, the dependence of the amplitude and frequency of oscillation of temperature and velocity disturbances on effective parameters on properties changes was evaluated and the results were analyzed. It can be said that critical Rayleigh number behavior is completely inverse in relation to the thermal emission and kinematic viscosity coefficients, and therefore their simultaneous effect in solving the equations will lead to a decrease in the critical interval of the oscillation.

In this paper some results about the Hyers-Ulam-Rassias stability for the Linear functional equations in general form and its Pexiderized can be proved for given functions on general domain to a complex Banach spaces under some suitable conditions. In connection with the problem of G. L. Forti in the 13st ICFEI we consider the common stability for the systems of functional equations and our aim is to establish some common Hyers-Ulam-Rassias stability for systems of homogeneous Linear functional equations. The results is applied to the study of some superstability results for the exponential functional equation.

In this paper, a class of Linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new system by using matrix decomposition and Linear matrix inequality (LMI) technique. Some numerical examples are given to illustrate the efficiency of our method.

In the present work we continue studying the solvability of the Linear functional equations åNj=1Cj F o aj=H and also the strong and weak stability of the corresponding operator P (see the definition below). By analogy with the Cauchy and Jensen operators once more model operator pˆis considered, and the stability problems as well as some solvability problems for pˆ are studied. Several unsolved problem of a general character are formulated.