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This paper is concerned with the problem of stochastic stability analysis for fractional-order Markovian jumping complex-valued neural networks (MJCVNNs) with time-varying delays. The novelty of this study is emphasized in two phases. In first phase, MJCVNNs is considered in the form of fractional-order systems. Secondly, complex-valued Wirtinger based integral inequality is newly constructed. The existence and uniqueness conditions of the proposed systems are derived based on the homeomorphism theorem in the complex domain. Then, the stochastic stability condition is derived in terms of linear matrix inequalities (LMIs) for the MJCVNNs by employing Lyapunov indirect method. The feasibility of the derived conditions is verified by the numerical examples and their simulation results are demonstrated to show the effectiveness of the fractional-order derivatives and proposed approach.

This paper is concerned with the problem of network-based filtering for a discrete-time positive system subject to random communication delays and deception attacks. The delays and attacks are considered as phenomena occurring randomly via network communication, either passively or actively, and thus they can be suitably characterized by mutually independent Markov stochastic process and Bernoulli random variable. A novel resilient filter of a mode-dependent structure based on delayed and tampered sensor measurement is proposed. With such a mode-dependent filter, the network-based filtering error system is modeled by an augmented Markov jump linear system. Criteria by means of linear programming are then developed to determine the filter gain matrices such that the filtering error system guarantees its resiliency in terms of stochastic stability under a prescribed l1-gain while mitigating the simultaneous effects of random communication delays, deception attacks, disturbance, noise, and jumping system parameters. An illustrative example is given to test the feasibility of the conditions and verify the effectiveness of the resilient filter.

In this paper, the stochastic stability problem for a class of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump is discussed. The uncertainty of semi-Markov jump refers to that the partial information on transition rates are incompletely known. Firstly, an extended reciprocally convex combination inequality with less conservative is provided. Secondly, by constructing an eligible stochastic Lyapunov–Krasovskii functional with considering more information about various time delays, uncertain semi-Markov jumping parameters, some stability criterions are derived via utilizing the improved inequality together with some integral inequalities. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.

In this paper, the stability problem is investigated for Hopfield neural networks (HNNs) perturbed by Poisson noises. Note that Poisson process can better reflect the dynamical behaviors of jump stochastic noises which exist widely in neurons. A stability criterion for HNNs perturbed by Poisson noises is presented by employing a combination of the martingale theory and measure theory. Finally, a simulation example is given to illustrate the effectiveness of the proposed stability criteria.

This paper is concerned with the finite-time synchronization for a class of stochastic genetic regulatory networks (GRNs). The purpose of the addressed problem is to design a controller that can synchronize the concentration of the mRNA and the protein of GRNs in finite time with probability. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are first established for ensuring the finite-time stochastic stability of synchronization error in probability. Then, the gain parameters of the controller are obtained by solving a linear matrix inequality and the robust finite-time synchronization is guaranteed for GRNs with uncertain parameters. Compared with the previous references, a continuous finite-time controller is designed to achieve the synchronization objective and a constructive method that may accelerate the convergence is discussed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

This paper deals with the problem of robust stochastic stability analysis for a class of neutral-type uncertain neural networks with Markovian jumping parameters and time-varying delays. By introducing an novel mode-dependent Augmented Lyapunov-Krasovskii functional with delay partitioning and Wirtinger-based integral inequality techniques, some improved delay-dependent stochastically stable conditions are proposed in the form of LMIs. Numerical simulations are provided to show the effectiveness and less conservatism of the results.

This paper considers linear quadratic (LQ) optimal control problems based on state observer for a class of discrete-time system over lossy data network. Both sensor data and control commands are transmitted by the same network. And the packets may be randomly lost according to the Bernoulli distribution. In the infinite horizon expected total cost we derive expressions for computing the corresponding controller gain. And the hold-input compensation strategy is applied to the closed system in which the previous control signal is used when packet dropped. Moreover, illustrative example is presented to demonstrate the effectiveness of the proposed results.

In this paper, the problem of stochastic stability of neutral-type neural networks with Markovian jumping parameters is considered. By choosing an mode-dependent Lyapunov–Krasovskii functional, novel delay-dependent stochastically stable conditions are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.

This paper studies the robust stochastic stability of uncertain stochastic genetic regulatory networks with disturbance attenuation. A novel delay-dependent robust stability condition with disturbance attenuation, in the form of linear matrix inequalities (LMIs) is derived for the uncertain stochastic genetic networks with time-varying delays and intrinsic and extrinsic noises. These stability conditions can be tested efficiently by the available commercial software packages such as Matlab LMI Control Toolbox. Two numerical examples with simulations are given to illustrate the effectiveness and validity of the derived theoretical results.

This paper is concerned with the problem of finite-time stability analysis for uncertain stochastic delayed reaction-diffusion genetic regulatory networks. The parameter uncertainties are assumed to be norm-bounded, and the time delays are assumed to be time-varying. Based on the Lyapunov functional method, sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. When there are no norm-bounded parameter uncertainties in the networks, a finite-time stochastic stability condition is also established. All the conditions are diffusion-dependent as well as delay-dependent. Numerical examples are given to illustrate the effectiveness of the proposed results.

This paper considers a stochastic neural network (SNN) with infinite delay. Some sufficient conditions for stochastic stability, stochastic asymptotical stability and global stochastic asymptotical stability, respectively, are derived by means of Lyapunov method, Ito formula and some inequalities. As a corollary, we show that if the neural network with infinite delay is stable under some conditions, then the stochastic stability is maintained provided the environmental noises are small. Estimates on the allowable sizes of environmental noises are also given. Finally, a three-dimensional SNN with infinite delay is analyzed and some numerical simulations are illustrated to show our results.

In this paper, we investigate robust stochastic stability of Markovian switching genetic regulatory networks with discrete and distributed delays. Different from previous correspondingly works, discrete and distributed delays are involved to describe the concentration of macromolecule for genetic networks. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability in the mean square of the stochastic genetic networks with Markovian switching. An illustrative example is given to show the effectiveness of our theoretical results.

In this paper, the stochastic stability problem of neutral-type impulsive neural networks (NINNs) with mixed time-varying delays and Markovian jumping is investigated. By utilizing the Lyapunov-Krasovkii functional approach and linear matrix inequality (LMI) technique, we obtain some novel globally exponentially stable results. Delay-dependent sufficient condition for the above problem is obtained, which is usually less conservative than delay-independent ones. An example is given to show the effectiveness of the obtained results.

This paper investigates the problem of stability analysis for Markovian jumping Hopfield neural networks (MJHNNs) with constant and distributed delays. Some new delay-dependent stochastic stability criteria are derived based on a novel Lyapunov-Krasovskii functional (LKF) approach. These new criteria based on the delay partitioning idea prove to be less conservative, since the conservatism could be notably reduced by thinning the delay partitioning. Numerical examples are provided to show the effectiveness and advantage of the proposed techniques.

In this paper, we study the delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, some numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature. Furthermore, the supplementary requirement that the time derivative of discrete time-varying delays must be smaller than the value one is not necessary to derive the results in this paper.

This paper is concerned with the robust asymptotic stability analysis for uncertain genetic regulatory networks with both interval time-varying delays and stochastic noise. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges of delays, some new delay-range-dependent and rate-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the delayed genetic regulatory networks to be robustly asymptotically stable in the mean square. As a result, the new criteria are applicable to both fast and slow time-varying delays. Five numerical examples are also used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.