STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology

An improved stability criterion for discrete-time time-delayed Lur’e systemwith sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur\u27e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach

On Less Conservative Stability Criteria for Neural Networks with Time-Varying Delays Utilizing Wirtinger-Based Integral Inequality

This paper investigates the problem of stability analysis for neural networks with time-varying delays. By utilizing the Wirtinger-based integral inequality and constructing a suitable augmented Lyapunov-Krasovskii functional, two less conservative delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). Three numerical examples are included to explain the superiority of the proposed methods by comparing maximum delay bounds with the recent results published in other literature

Dissipative Stabilization of Linear Systems with Time-Varying General Distributed Delays (Complete Version)

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovski\u{i} functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.Comment: Accepted by Automatic

Improved Results on H∞ State Estimation of Static Neural Networks with Time Delay

This paper studies the problem of ∞ state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribed ∞ performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results

Pinning Cluster Synchronization in Linear Hybrid Coupled Delayed Dynamical Networks

The problem on cluster synchronization will be investigated for a class of delayed dynamical networks based on pinning control strategy. Through utilizing the combined convex technique and Kronecker product, two sufficient conditions can be derived to ensure the desired synchronization when the designed feedback controller is employed to each cluster. Moreover, the inner coupling matrices are unnecessarily restricted to be diagonal and the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which greatly improve the present methods. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism