Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

Risk-based water quality decision-making under small data using Bayesian network

A knowledge-based network for Section Yidong Bridge,Dongyang River,one tributary of Qiantang River,Zhejiang Province,China,is established in order to model water quality in areas under small data.Then,based on normal transformation of variables with routine monitoring data and normal assumption of variables without routine monitoring data,a conditional linear Gaussian Bayesian network is constructed.A "two-constraint selection" procedure is proposed to estimate potential parameter values under small data.Among all potential parameter values,the ones that are most probable are selected as the "representatives".Finally,the risks of pollutant concentration exceeding national water quality standards are calculated and pollution reduction decisions for decision-making reference are proposed.The final results show that conditional linear Gaussian Bayesian network and "two-constraint selection" procedure are very useful in evaluating risks when there is limited data and can help managers to make sound decisions under small data.

Delay and Its Time-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating Actuators

This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities （LMIs） with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov- Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.

Existence and Uniqueness of Positive Solutions for Some Singular Boundary Value Problems with Linear Functional Boundary Conditions

By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Continuous Coefficients

A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.

The Inductive Blockwise Alperin Weight Condition for PSL（3, q）

The blockwise Alperin weight conjecture assets that for any finite group G and any prime l, the number of the Brauer characters in an l-block B equals the number of the G-conjugacy classes of l-weights belonging to B. Recently, the inductive blockwise Alperin weight condition has been introduced such that the blockwise Alperin weight conjecture holds if all non-abelian simple groups satisfy these conditions. We will verify the inductive blockwise Alperin weight condition for the finite simple groups PSL（3, q） in this paper.