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This article studies the robust exponential stability and Takagi–Sugeno (T–S) fuzzy control synthesis for networked control systems via ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance. The main aim of this paper is to design fuzzy controllers with less conservative results. Novel weighted integral inequalities (WIIs) are proposed based on Wirtinger's integral inequalities. The T–S fuzzy approach expresses nonlinear systems as linear submodels with IF–THEN rules for deriving the stability conditions. Then, by constructing a suitable Lyapunov–Krasovskii functional (LKF) and applying new WIIs, improved exponential stability and stabilization criteria are established in the form of linear matrix inequalities (LMIs). Three examples are provided to demonstrate the advantages and usefulness of the proposed novel method. Two are application‐oriented examples, such as the variable speed wind turbine (VSWT) system and nonlinear mass‐spring (NMS) system. [ABSTRACT FROM AUTHOR]

The paper considers the finite-time stability of descriptor time-delay systems. Firstly, we establish a set of exponentially weighted orthogonal polynomials, and based on this, we obtain a new exponentially weighted inequality(EWI). Secondly, an augmented Lyapunov-like functional (LLF) is established driven by the presented EWI. Finally, by applying the EWI and the LLF, some sufficient conditions for ensuring the finite-time stability of the system are obtained. A small partial element equivalent circuit model and two numerical examples are used to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a weighted integral inequality to derive decay estimates for the quasilinear viscoelastic wave equation with variable density |ut|ρutt−Δu−Δutt+∫0tg(t−s)Δu(s)ds=0in Ω×(0,∞) $$\begin{aligned} \vert u_{t} \vert ^{\rho }u_{tt}-\Delta u-\Delta u_{tt}+ \int^{t}_{0}g(t-s)\Delta u(s)\,ds=0 \quad \text{in } \varOmega \times (0, \infty ) \end{aligned}$$ with initial conditions and boundary condition, where g is a memory kernel function and ρ is a positive constant. Depending on the properties of convolution kernel g at infinity, we establish a general decay rate of the solution such that the exponential and polynomial decay results in some literature are special cases of this paper, and we improve the integral method used in the literature.

This article evaluates the exponential dissipativity and passivity criterions for generalized bidirectional associative memory neural networks (BAMGNNs) including interval time-varying delayed signals. Exponential dissipativity and passivity criterions are proposed by making suitable Lyapunov–Krasovskii functional and proposing a novel approach. The improved reciprocally convex combination and weighted integral inequality techniques are utilized to obtain new exponential dissipativity and passivity conditions of such delayed BAMGNNs. The feasibility of the obtained results is clearly demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of exponential stability analysis of linear time-delay systems. First, based on the Gram-Schmidt-based integral inequality and the Taylor expansion of exponential function, we develop a new weighted multiple integral inequality called Taylor expansion-based weighted integral inequality. Second, a new Lyapunov-krasovskii functional is constructed, and then, with the help of the Taylor expansion-based inequality, a new exponential stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are presented to show the effectiveness of the newly established stability criterion. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time synchronization problem of coupled hierarchical hybrid delayed neural networks. This coupled hierarchical hybrid neural networks consist of a higher level switching and a lower level Markovian jumping. The time-varying delays are dependent on not only switching signal but also jumping mode. By using a less conservative weighted integral inequality and stochastic multiple Lyapunov–Krasovskii functional, new finite-time synchronization criteria are obtained, which makes the state trajectories be kept within the prescribed bound in a time interval. Finally, an example is proposed to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM PUBLISHER]

This article explores the extended dissipativity conditions for generalised neural networks (GNNs) including interval time-varying delays. Extended dissipativity criterions are proposed by making proper Lyapunov-Krasovskii functional. The improved reciprocally convex combination and weighted integral inequality techniques are together applied in main results to establish the new extended dissipativity conditions of delayed GNNs. Finally, the feasibility and superiority of the proposed novel approach is clearly shown by numerical examples. [ABSTRACT FROM AUTHOR]

This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov–Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

Consider the Korteweg-de Vries equation u + u + uu = 0 and its generalization u+ u + f( u) x = 0. For the solutions of these equations, weighted identities (differential and integral) are obtained. These identities make it possible to establish the blow-up (in finite time) of the solutions of certain boundary-value problems. [ABSTRACT FROM AUTHOR]

We first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in Ls(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings. [Copyright &y& Elsevier]