Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case of which is Exponential stability) and input-output stability. This paper develops fuzzy Lyapunov stability through investigating the concept of stability for finite-dimensional systems under uncertainty and provides some related theorems. Considering the capability of fuzzy differential systems for modeling uncertainty and processing vague or subjective information in mathematical models, Exponential stability and Lyapunov stability of fuzzy differential systems are presented. Also, numerical examples are given to support the theoretical ‎results.

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.

Teleoperation systems have attracted more attention in processes that human operator’s availability is difficult. In this paper, using retarded functions, teleoperation systems have been modeled as a special case of Network Control Systems (NCS) with nonuniform sampling and network delays. It is assumed that slave and master robots are linear and continues-time systems and input-delay approach is used for the stability analysis. Using the proposed Lyapunov function, the sufficient conditions for the stability of discrete network-based teleoperation system is proposed. It will be represented that the proposed conditions are less conservative than previous recent researches. Also an upper bound of sampling time for discrete control signals is computed in a manner that does not disturb the stability conditions. To meet this condition the problem is defined as the convex optimization program and is represented by the LMI terms. In the simulation part, the behavior of the teleoperation system under the nonuniform sampling is represented and the effect of sampling time on the trade-off between the stability and transparency has been studied.

The stochastic reaction diffusion systems may suffer sudden shocks, in order to explain this phenomena, we use Markovian jumps to model stochastic reaction diffusion systems. In this paper, we are interested in almost sure Exponential stability of stochastic reaction diffusion systems with Markovian jumps. Under some reasonable conditions, we show that the trivial solution of stochastic reaction diffusion systems with Markovian jumps is almost surely Exponentially stable. An example is given to illustrate the theory.

In this paper, we consider a nonautonomous viscoelastic wave equation with linear damping and delayed terms. Under some appropriate assumptions, we prove the global existence using the semi-group theory. Furthermore, for a small enough coefficient of delay, we obtained a stability result via a suitable Lyapunov function where the kernel function decays Exponentially.

This study examines the balanced Maruyama with two step approximations of stochastic Hopfield neural networks with delay. The main aim of this paper is to discover the conditions under which the exact solutions remain stable for the balanced Maruyama with two-step approximations of stochastic delay Hopfield neural networks (SDHNN). The semi martingale theorem for convergence is used to demonstrate the almost sure Exponential stability of balanced Maruyama with two-step approximations of stochastic delay Hopfield networks. Additionally, the numerical balanced Euler approximation's stability conditions are compared. Our theoretical findings are illustrated with numerical experiments.

Menendez (2000) published a paper on Shannon's entropy in Exponential family and discussed some properties of them. He introduced an asymptotic distribution for it. In this paper we present an entropy characterization of general Exponential model so that Menendez definition is particular state of it. Also we introduced another asymptotic distribution for (H(^q) - H (q0)),where H (q) is Shannon's entropy of X with distribution ¦q (x) , and ^q is MLE of q.

The State-Dependant Riccati Equation method has been frequently used to design suboptimal controllers applied to nonlinear dynamic systems. Different methods for local stability analysis of SDRE controlled systems of order higher than two such as the attitude dynamics of a general rigid body have been developed in the literature; however, it is still difficult to show global stability properties of closed-loop system with this controller. In this paper, a reduced-form of SDRE formulation for attitude dynamics of a general rigid body is achieved by using Input-State Linearization technique and solved analytically. By using the solution matrix of the reduced-form SDRE in properly defined Lyapunov functions, a class of nonlinear controllers with global stability properties is developed. Numerical simulations are performed to study the stability properties and optimality for attitude stabilization of a general rigid body, and it is concluded that the designed controllers have the capability to provide a balance between optimality and proper stability characteristics.

The aim of this study was to investigate the effect of using portulaca oleracea as a source of plant antioxidants for feeding fattening male lambs, on carcass traits, meat quality, and oxidative stability. Twenty-one male lambs with an average weight of 24±1.5 kg and 150±15 days old were fed with one of the experimental rations included a diet without portulaca oleracea as control, a diet containing 7.5%, and a diet containing 15% portulaca oleracea, for 84 days. The muscle (Longissimus dorsi) samplewas used to determine pH, chemical composition, colorimetric properties, and oxidative stability of meat. Meat lipid oxidation was determined after 1, 7, and 30 days of refrigerated storage using thiobarbituric acid (TBARS). The use of portulaca oleracea in diets improved meat color characteristics such as L, chroma, and Hue. The highest ash concentration and the lowest meat moisture were observed in the treatment of 15% portulaca oleracea (P<0.05). Meat pH was the lowest in the first hour after slaughter but did not differ at 24 h. Compared to the control, in both treatment groups feeding the lambs with portulaca significantly reduced the concentration of Malondialdehyde in the meat of the lambs and increased the meat oxidative stability (P<0.05). The results of this experiment showed that feeding portulaca oleracea by improving properties such as color and increasing the meat oxidative stability improves meat quality, which may have lead to an increase in its nutritional value in terms of human health.

We introduce a new wrapped Exponential distribution named transmuted wrapped Exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped Exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Ré nyi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.