In this work we prove that for any measurable admissible control w (.) and for any e>0 there exists piecewise constant admissible control w¯ (.) such that for fuzzy solutions of control fuzzy linear system are e-closed.

In this study, we introduce the Non-monotonic Lyapunov (NML) approach, aimed at stability examining and designing stabilizable controller for a specific category of discrete piecewise affine dynamical systems. Traditional Lyapunov techniques are often characterized by their conservative nature, which has spurred the creation of more adaptable methods like NML. A key distinction of the NML approach is its lack of reliance on strict monotonicity when establishing the decrease of a Lyapunov functional. As a result, we derive new stability and stabilization criteria based on the NML framework, expressed as LMIs (linear matrix inequalities) tailored for piecewise affine systems. This NML-based methodology is employed to develop a semi-PID controller which is also able to handle multi-input multi-output (MIMO) piecewise linear systems. Additionally, we present an algorithm for optimal semi-PID controller design, aimed at achieving both optimal trajectories and refined control signals. The effectiveness of this innovative approach is highlighted through various examples and simulation results, demonstrating its significant contributions to PID design within complex systems. The findings underscore the practical applicability and advantages of the NML method in enhancing control strategies.

The problem of finding the minimum cost multi-commodity flow in an undirected and complete network is studied when the link costs are piecewise linear and convex. The arc-path model and overflow model are presented to formulate the problem. The results suggest that the new overflow model outperforms the classical arc-path model for this problem. The classical revised simplex, Frank and Wolf and a heuristic method are compared for the problem.

This paper presents a new approach to estimate and to enlarge the domain of attraction for a planar continuous-time piecewise affine system. Various continuous Lyapunov functions have been proposed to estimate and to enlarge the system’s domain of attraction. In the proposed method with a new vision and with the aids of a discontinuous piecewise quadratic Lyapunov function, the domain of attraction at the origin is enlarged by designing a state feedback controller. This paper shows that the continuity of the Lyapunov function on the boundaries, increases the conservativeness in estimating the domain of attraction, and gives more powerful search ability to the domain of attraction estimation algorithm by relaxing this continuity condition. The simulation results show the superiority of the proposed method so that using this method the larger estimation of the domain of attraction is obtained than continuous one.

The present study investigates whether the basic assumption in the Jones model, which normal accruals are a linear function of change in sales, is empirically valid. It also discusses and addresses the implications of the assumption violation in the earnings management detection tests. The research employs a sample of 2832 observations of the annual information of firms listed in Tehran Stock Exchange and Iran Fara Bource for the period of 2002 to 2017. The findings suggest that normal accruals follow a piecewise linear function with respect to sales changes. The results also suggest that the Jones model generates predictable systematic measurement error, which is consistent with its failure in capturing the accruals nonlinear behavior. The results of a Monte Carlo simulation of the type I error show that the level of abnormal accruals are understated for extreme sales growth and overstated for medium sales growth. The research highlights the importance of controlling the asymmetric behavior of normal accruals, especially in studies where earnings management incentives are correlated with sales growth.

One of the most widely used statistical topics in research fields is regression problems. In these models, the basic assumption of model errors is their normality, which, in some cases, is different due to asymmetry features or break points in the data. Piecewise regression models have been widely used in various fields, and it is essential to detect the breakpoint. The break points in piecewise regression models are necessary to know when and how the pattern of the data structure changes. One of the major problems is that there is a heavy tail in these data, which has been solved by using some distributions that generalize the normal distribution. In this paper, the piecewise regression model will be investigated based on the scale mixture of the normal distribution. Also, this model will be compared with the standard piecewise regression model derived from normal errors.