Extended dissipative state estimation for memristive neural networks with time-varying delay

Finite-time synchronization of reaction-diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme

The finite-time synchronization issue of reaction-diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2ⁿ controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.

Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay

The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.

Aperiodic sampled-data control for local stabilization of memristive neural networks subject to actuator saturation: Discrete-time Lyapunov approach

In this paper, the local stabilization of memristive neural networks (MNNs) with actuator saturation is investigated via aperiodic sampled-data control. Inspired by the characteristic of the control scheme, a novel sampling-interval-dependent Lyapunov functional (SIDLF) is constructed. The main contribution of the developed Lyapunov functional lies in that the requirement on its positive definiteness is replaced by a looped condition. Then, using some inequality techniques and the discrete-time Lyapunov approach, two sufficient criteria are derived to ensure the locally asymptotical stability of the trivial solutions of closed-loop systems. A unified work is developed that can deal with the presence of the saturation nonlinearity effects, aperiodic sampled-data control, as well as SIDLF. Additionally, two convex optimization schemes, aiming at enlarging the admissible initial region (AIR) and maximizing the upper bound of sampling interval, are respectively presented for designing the desired saturated sampled-data controller gains. A quantitative relationship between the maximum sampling interval and AIR is revealed. Finally, two numerical examples are given to illustrate the advantages and effectiveness of the derived theoretical conclusions.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov-Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

Finite-time non-fragile extended dissipative control for T-S fuzzy system via augmented Lyapunov-Krasovskii functional

The problem of non-fragile control for T-S fuzzy systems with parameter uncertainties is investigated in this paper. The focus is to construct an augmented Lyapunov-Krasovskii functional(LKF), single integral terms are processed by the method of an improved reciprocally convex inequality and integration by parts, which is derived to a new ht-depended stability criteria that finite-time bounded with extended dissipative for the closed-loop system. Furthermore, by using the linear matrix inequalities(LMIs), we can get the desired gain matrices of T-S fuzzy system. It is worth noting that these condition can derive to less conservative results than those existing approaches. And numerical examples are used to demonstrate the feasibility and superiority of the results.

An improved result on synchronization control for memristive neural networks with inertial terms and reaction-diffusion items

This paper investigates the synchronization issue of the memristive neural networks (MNNs) with inertial terms and reaction-diffusion items. In order to smoothly derive the controller gains and obtain an excellent control effect, the desired controller that contains a discontinuous function is proposed. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining the inequality techniques, several sufficient conditions in terms of algebraic inequalities are obtained to guarantee the synchronization of the proposed drive and response systems. Finally, three numerical simulations are exploited to support the acquired theoretical results.

An Arcak-type state estimation design for time-delayed static neural networks with leakage term based on unified criteria

The issue of unified dissipativity-based Arcak-type state estimator design for delayed static neural networks (SNNs) with leakage term and noise distraction was considered here. An Arcak-type state observer, which is compact than the usually used Luenberger-type state estimator, is selected to implement the subject of a unified dissipativity performance of SNNs. This paper primarily concentrates on the issue of Arcak-type state estimator of delayed SNNs involving leakage delay. The first attempt is made to tackle the Arcak-type state estimator of SNNs with time delay in leakage term in this paper based on the unified criteria, by constructing a novel Lyapunov functional together with newly improved integral inequalities. As a result, a novel unified state estimation criterion is launched in the form of linear matrix inequalities (LMIs) and put forward to justify the dynamics of error system is extended dissipative with the influence of leakage term and estimator gain matrices K¯₁ and K¯₂. Finally, an interesting simulation study is ultimately explored to show the performance of the established unified dissipativity-based theoretical results, in which, comparison results are also made together with recent works as a special case.

Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems with time-varying delay

Though many studies are focused on the stabilization of nonlinear systems with time-varying delay, they fail to involve the dynamic regulation without on-line optimization commonly. For this sake, feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem are employed here to verify that the multi-dimensional Taylor network (MTN) controller can stabilize the single input single output (SISO) nonlinear time-varying delay systems through dynamic regulation of the system output with no need for on-line optimization. Here, the design of the controller is transformed into a convex optimization problem, which is tackled by means of the appropriate optimization method. Like its PD-like controller peers, the MTN controller functions well in eliminating the dependence on the system model. The effectiveness of the proposed approach is demonstrated and confirmed via two examples.

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.