Terminal sliding mode control with self-tuning for coronary artery system synchronization

A terminal sliding mode (TSM) control with self-tuning gain algorithm is proposed for the synchronization of coronary artery system under the existence of the unmodeled dynamics and the external disturbance. Considering the sliding mode dynamics of system, a criterion of selecting the parameters is derived to reach the point of equilibrium in the finite time. The theoretic analysis based on Lyapunov theory proved that the systems with the proposed TSM control with self-tuning scheme could be stabilized in finite time. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system in finite time. This information about the bound of unmodeled dynamics and the external disturbance is not needed in advance through self-tuning the gains of controller. The results for coronary artery system synchronization simulation show that the proposed TSM controller with self-tuning achieves better robustness and adaptation against unmodeled dynamics and the external disturbance, which offer the theory basis on curing myocardial infarction.

Extended dissipative state estimation for uncertain discrete-time Markov jump neural networks with mixed time delays

This paper is concerned with the problem of extended dissipativity-based state estimation for uncertain discrete-time Markov jump neural networks with finite piecewise homogeneous Markov chain and mixed time delays. The aim of this paper is to present a Markov switching estimator design method, which ensures that the resulting error system is extended stochastically dissipative. A triple-summable term is introduced in the constructed Lyapunov function and the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term. The extended dissipativity criterion is derived in form of linear matrix inequalities. Numerical simulations are conducted to demonstrate the effectiveness of the proposed method.

Complete stability of delayed recurrent neural networks with Gaussian activation functions

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3^k equilibrium points with 0≤k≤n, among which 2^k and 3^k-2^k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results.

Mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching based on vector Lyapunov functions

This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results.

Dynamical Behavior of Delayed Reaction-Diffusion Hopfield Neural Networks Driven by Infinite Dimensional Wiener Processes

In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.

Observer-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem.

Global synchronization of discrete-time coupled neural networks with Markovian switching and impulses

This paper is concerned with the problem of synchronization analysis for discrete-time coupled neural networks. The networks under consideration are subject to: (1) the jumping parameters that are modeled as a continuous-time, discrete-state Markov process; (2) impulsive disturbances; and (3) time delays that include both the mode-dependent discrete and distributed delay. By constructing suitable Lyapunov–Krasovskii functional and combining with linear matrix inequality approach, several novel criteria are derived for verifying the global exponential synchronization in the mean square of such stochastic dynamical networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. A simulation example is presented to show the effectiveness and applicability of the obtained results.

Stochastic stability of delayed neural networks with local impulsive effects

In this paper, the stability problem is studied for a class of stochastic neural networks (NNs) with local impulsive effects. The impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants. Hence, the impulses here can encompass several typical impulses in NNs. The aim of this paper is to derive stability criteria such that stochastic NNs with local impulsive effects are exponentially stable in mean square. By means of the mathematical induction method, several easy-to-check conditions are obtained to ensure the mean square stability of NNs. Three examples are given to show the effectiveness of the proposed stability criterion.

New Results on Passivity Analysis of Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

The passivity problem for a class of stochastic neural networks systems (SNNs) with varying delay and leakage delay has been further studied in this paper. By constructing a more effective Lyapunov functional, employing the free-weighting matrix approach, and combining with integral inequality technic and stochastic analysis theory, the delay-dependent conditions have been proposed such that SNNs are asymptotically stable with guaranteed performance. The time-varying delay is divided into several subintervals and two adjustable parameters are introduced; more information about time delay is utilised and less conservative results have been obtained. Examples are provided to illustrate the less conservatism of the proposed method and simulations are given to show the impact of leakage delay on stability of SNNs.

Finite-time boundedness filtering for discrete-time Markovian jump system subject to partly unknown transition probabilities

This paper investigates the problem of finite-time boundedness filtering for discrete-time Markovian jump system subject partly unknown transition probabilities. By using the multiple Lyapunov function approach, a novel sufficient condition for finite-time bounded of H∞ filtering is derived and the system trajectory stays within a prescribed bound during a specified time interval. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.

Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays

In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov-Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results.

Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals

This paper is concerned with the problem of finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed. Based on the derived condition, the reliable H∞ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.