This paper is concerned with the delay-dependent stability of systems with time-varying delays. The novelty relies on the use of the second-order Bessel-Legendre integral inequality which is less conservative than the Jensen and Wirtinger-based inequalities. Unlike similar contributions, the features of this inequality are fully integrated into the construction of augmented Lyapunov-Krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities. The stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method.

The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite delays. In this paper, we first present a generalized integral inequality and its double integral extension. It is shown how these inequalities can be applied to improve the stability result for linear continuous-time systems with gamma-distributed delays. Then, for the discrete-time counterpart we provide an extended Jensen summation inequality with infinite sequences, which leads to less conservative stability conditions for linear discrete-time systems with poisson-distributed delays. The improvements obtained thanks to the introduced generalized inequalities are demonstrated by examples.

The fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh's decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, the existing methods and the results will be limited when the objective functions (or the constraint functions) of a fuzzy linear programming contain generalized fuzzy numbers. In this paper, we first investigate the approximate representation of the fully fuzzy constraints and the transformation theorem of the fully fuzzy linear programming problem by means of the definition of the extended LR-fuzzy numbers. At the same time, the fully fuzzy linear programming problem is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers proposed in this paper. Finally, the results obtained are compared with the existing work, and some numerical examples are given.

In order to improve the comprehensive combustion efficiency of the steam coal and reduce waste of resources, combustion experiments of petroleum coke and coal gangue were carried out by thermogravimetric analyser at different proportions and heating rates. Combustion characteristic curves (TG, DTG, DTA) and combustion characteristic parameters of the blended samples were analysed by thermogravimetric analysis and thermogravimetric analysis. The optimum combustion ratio and combustion characteristic parameters of the blended samples were explored. Experiments show that the combustion performance of petroleum coke and coal gangue is the best when the mixture ratio of petroleum coke and coal gangue is 4:1 in air atmosphere and the flow rate is 30ml/min, and the combustion characteristics of petroleum coke and coal gangue are better than that of single sample. The burning effect of the mixed fuel is the best. The exothermic area of 15°C/min and 25°C/min is greater than that of 20°C/min, which indicates that the heating rate of 20°C/min is not conducive to exothermic.

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