Exponential stability for time-delay neural networks via new weighted integral inequalities

Weighted Orthogonal Polynomials-Based Generalization of Wirtinger-Type Integral Inequalities for Delayed Continuous-Time Systems

In the past three years, many researchers have proven and/or employed some Wirtinger-type integral inequalities to establish less conservative stability criteria for delayed continu\-ous-time systems. In this present paper, we will investigate weighted orthogonal polynomials-based integral inequalities which is a generalization of the existing Jensen's inequalities and Wirtinger-type integral inequalities.

New summation inequalities and their applications to discrete-time delay systems

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.

通过贝塞尔 - 勒让德不等式研究一类非线性时滞系统的耗散性

Dissipativity properties of a class of nonlinear time-delay systems via Bessel-Legendre inequalities

研究一类含多个离散时滞的非线性时滞系统的耗散性，利用贝塞尔 - 勒让德不等式得出时滞依赖和时滞独立耗散性的充分条件，线性系统条件可用线性矩阵不等式求解。

Multiple summation inequalities and their application to stability analysis of discrete-time delay systems

This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen's and Wirtinger's inequalities, as well as the recently presented inequalities for single and double summation in P.T. Nam, H. Trinh, P.N. Pathirana, Discrete inequalities based on a multiple auxiliary functions and their applications to stability analysis of time-delay systems, Journal of the Franklin Institute, (2015). The present paper aims at showing that the proposed set of suff…

A note on relationship between some bounding inequalities in stability analysis of time-delay systems

In this paper, an extension of the generalized free matrix based inequality is introduced in a unified form suitable for the estimation of integrals and sums of quadratic functions. The equivalences of several known variants are shown, including the free matrix based inequalities and its simplified form. Secondly, the relationship between the (simplified) free matrix based estimation and the combination of the Bessel-based inequality with different bounding inequalities affine in the length of the intervals are investigated.

A remark on optimal weighted Poincaré inequalities for convex domains

We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincaré inequalities. The key point is the study of an optimal weighted Wirtinger inequality.