In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in Schulz and Tiedemann \cite{schulz2006}. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized qualitative results to express the explicit formula for the directional derivative of the local optimal value function with respect to the underlying probability measure. The derivative is used to construct the bounds. Similarly, we can approximate the behavior of the local optimal value function with respect to the changes of the risk-aversion parameter which determines our aversion to risk.
The paper addresses the prediction of roll-waves occurrence in mud-flows. The spatial growth of a point-wise disturbance is analytically described, based on the linearized flow model of a Herschel and Bulkley fluid, in the neighborhood of an initial uniform base condition. The theoretical achievements allow to generalize to mud-flows the minimum channel criterion commonly used for the prediction of roll-waves in clear-water. The applicability of the criterion is discussed through the comparison with literature laboratory data concerning unstable flows without rollwaves.
This paper proposes new stability conditions for interval type-2 fuzzy-model-based (FMB) control systems. The type-1 T-S fuzzy model has been widely studied because it can represent a wide class of nonlinear systems. Many favorable results for type-1 T-S fuzzy model have been reported. However, most of conclusions for type-1 T-S fuzzy model can not be applied to nonlinear systems subject to parameter uncertainties. In fact, Most of the practical applications are subject to parameters uncertainties. To address above problem, an interval type-2 T-S fuzzy model has been proposed to approximate nonlinear systems subject to parameter uncertainties, and stability conditions for interval type-2 FMB control systems have also been presented in the form of linear matrix inequalities (LMIs). The aim of this paper is to relax the existing stability conditions. The new stability conditions in terms of LMIs are derived to guarantee the stability of interval type-2 FMB control systems. The theoretical poof is given to show the proposed conditions reduce the conservativeness in stability analysis. Several numerical examples are also provided to illustrate the effectiveness of the proposed conditions.