Markovian Jumping Parameters Research Articles

New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays

This paper examines the problem of asymptotic stability criteria for Markovian jump generalized neural networks with successive time-varying delay components. Generalized neural networks consist of a finite number of modes, which may jump from one mode to another according to a Markovian chain with known transition probability. By constructing novel augmented Lyapunov–Krasovskii functionals (LKFs) with triple integral terms that contain more and more information on the state vectors of the NNs, the upper bound of the successive time-varying delays is formulated. By employing a new integral inequality technique, free-weighting matrix-based integral inequality approach, and Wirtinger double integral inequality technique and that is combined with the reciprocally convex combination approach to estimate the single and double integral terms in the time derivative of the LKFs, a new set of delay-dependent conditions for the asymptotic stability of the considered NNs are represented in the form of linear matrix inequalities. Finally, five numerical examples are given to verify the effectiveness of the proposed approach with a four-tank benchmark real-world problem.

State estimation of neutral Markovian jump systems: A relaxed L–K functional approach

This paper investigates the state estimation problem of uncertain neutral delay systems with Markovian jumping parameters. First, a novel Lyapunov–Krasovskii (L–K) functional containing the interconnected information between neutral and discrete delay is proposed. Then, based on Jensen’s integral and Wirtinger-based inequality, the obtained results are improved by relaxing the positive-definiteness restrictions on Lyapunov matrices. Third, the state estimators are designed to guarantee the asymptotic stability of the error state system. Finally, numerical examples are provided to show the effectiveness of the proposed results.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Delay-dependent robust resilient $$H_\infty $$ H ∞ control for uncertain singular time-delay system with Markovian jumping parameters

This paper is concerned with the delay-dependent robust resilient $$H_\infty $$ control problem for uncertain singular time-delay system with Markovian jumping parameters. First, a delay-dependent bounded real lemma in terms of linear matrix inequalities is established, which guarantees the nominal Markovian jump singular system to be regular, impulse free and stochastically stable. Then, based on this condition, sufficient conditions in terms of LMIs are given to ensure the existence of the desired robust resilient $$H_\infty $$ controllers. The uncertainties of the controllers are considered in two cases, that is the additive controller gain uncertainties and the multiplicative controller gain uncertainties. Finally, numerical examples illustrate the applicability of the results proposed in this paper.

Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback

This paper focuses on the analysis and design of dissipativity-based fault-tolerant controller for discrete-time nonlinear Markov jump singularly perturbed systems (MJSPSs) which are based on Takagi–Sugeno fuzzy model. A novel strategy is proposed to improve the upper bound of singular perturbation parameter (SPP) ϵ, and the fault-tolerant design is also introduced, namely the susceptible property of systems is made full consideration, to ensure the specified performance of a system. The aim is to design an optimized slow state feedback controller such that the stability of MJSPSs is guaranteed even in faulty case, and the upper bound of the SPP ϵ is improved simultaneously. Utilizing Lyapunov functional technique, a sufficient condition for the existence of controller is shown. Last but not least, the control issue of a series DC motor model as an illustrated example is given to explain the availability of the presented design scheme.

A state estimation H∞ issue for discrete-time stochastic impulsive genetic regulatory networks in the presence of leakage, multiple delays and Markovian jumping parameters

In this work, we probes the stability results of H∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.

Delay-dependent dissipativity criteria for Markovian jump neural networks with random delays and incomplete transition probabilities

In this paper, a new double integral inequality which covers the well-known Wirtinger’s double integral inequality has been developed to analyze the dissipativity behavior of continuous-time neural networks involving Markovian jumping parameters with some unknown transition probabilities and random delays. Based on this generalized double integral inequality, the dissipativity conditions are proposed in terms of linear matrix inequalities by constructing an appropriate Lyapunov–Krasovskii functional with some multiple integral terms under the consideration of free-matrix-based integral inequality and Finsler’s lemma approach. Finally, the effectiveness and the advantages of the proposed technique have been exhibited through numerical simulations.

Synchronization criteria for singular complex networks with Markovian jump and time-varying delays via pinning control

This paper makes a study on the problem of synchronization for singular complex networks with Markovian jumping parameters and mixed time-delays. The system consists of N nodes which switch from one mode to another according to a Markovian chain with known transition probability. Based on the strategies of pinning control, the singular complex networks are synchronized. A new type of criterion for synchronization can be obtained by means of utilizing the appropriate Lyapunov–Krasovskii function, the linear matrix inequality (LMI) approach, stochastic analysis techniques and the convexity of matrix functions. Finally, simulation examples are employed to demonstrate the effectiveness of the proposed method.

Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction–diffusion terms via sampled-data control

This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Stability analysis of inertial Cohen–Grossberg neural networks with Markovian jumping parameters

Abstract In this paper, we concentrate on the problem of global asymptotical stability for a class of Markovian jump inertial Cohen–Grossberg neural networks. The jumping parameters are described with a continuous-time, finite-state Markov chain. By adopting the method of model transformation, differential mean value theorem, Lyapunov stability theory and linear matrix inequality techniques, we derive some novel sufficient conditions to guarantee the global asymptotical stability for the addressed systems. It is worth mentioning that the model investigated in this letter comprises and generalizes many existing results in the previous literature. Finally, the effectiveness of the theoretical results is validated by numerical examples.

Robust Exponential Synchronization for Stochastic Delayed Neural Networks with Reaction–Diffusion Terms and Markovian Jumping Parameters

This paper investigates robust exponential synchronization for stochastic delayed neural networks with reaction–diffusion terms and Markovian jumping parameters driven by infinite dimensional Wiener processes. The novelty of this paper lives in the use of a new Lyapunov–Krasovskii functional and Poincare inequality to present some criteria for robust exponential synchronization in terms of linear matrix inequalities (LMIs) and matrix measure under Robin boundary conditions. Finally, two numerical examples are provided to illustrate the effectiveness of the easily verifiable synchronization LMIs in MATLAB toolbox.

Decay-rate-dependent conditions for exponential stability of stochastic neutral systems with Markovian jumping parameters

This note studies the problem of decay-rate-dependent exponential stability for neutral stochastic delay systems with Markovian jumping parameters. First, by introducing an operator D(xt,i) as well as a novel Lyapunov–Krasovskii functional, sufficient conditions for exponential stability of system with a decay rate are obtained. Second, the results are extended to the robust exponential estimates for uncertain neutral stochastic delay systems with Markovian jumping parameters. Finally, numerical examples are provided to show the effectiveness of the proposed results.

Distributed Control Design for Spatially Interconnected Markovian Jump Systems With Time‐Varying Delays

AbstractThis paper focuses on spatially interconnected Markovian jump systems with time‐varying delays. Firstly, a sufficient condition is given to check the well‐posedness, stochastic stability and contractiveness of spatially interconnected systems with the effect of time‐varying delays and Markovian jumping parameters. Secondly, the distributed controllers which inherit the structure of the plants are designed. A sufficient and necessary condition is proposed to guarantee the existence of the distributed controllers. Finally, an illustrative numerical example is given to show the effectiveness of the results.

Passivity-based non-fragile control for Markovian jump delayed systems via stochastic sampling

ABSTRACTThis paper studies the problem of non-fragile passive control for Markovian jump delayed systems via stochastic sampling. The Markovian jumping parameters, appearing in the connection weight matrices and in two additive time-varying delay components, are considered to be different. The controller is assumed to have either additive or multiplicative norm-bounded uncertainties. The sampled-data with stochastic sampling is used to design the controller by a discontinuous Lyapunov functional. This functional fully utilises the sawtooth structure characteristics of the sampling input delay. By using the matrix decomposition method and some newly inequalities, sufficient conditions are obtained to guarantee that for all admissible uncertainties the system is robustly stochastically passive. Illustrative examples are provided to show the effectiveness of the results.

Decentralized Event-Triggered Exponential Stability for Uncertain Delayed Genetic Regulatory Networks with Markov Jump Parameters and Distributed Delays

This paper is concerned with the stability problem for a class of decentralized event-triggered exponential stability for uncertain delayed genetic regulatory networks (GRNs) with Markov jump parameters and distributed delays. In order to reduce the information communication burden, the decentralized event-triggered mechanism is proposed in this paper. Exponential stability for the proposed GRNs are studied by the Lyapunov method and the matrix inequality techniques. Some new sufficient conditions are obtained to ensure the global exponential stability of the proposed GRNs. Furthermore, the proposed LMI results are computationally efficient which are easy to be verified via the Matlab LMI toolbox. In addition, four numerical examples are provided to illustrate the effectiveness of the theoretical results.

Stochastic stability analysis for a neutral-type neural networks with Markovian jumping parameters

Stochastic stability analysis for a neutral-type neural networks with Markovian jumping parameters

Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching

This paper deals with admissibility analysis for discrete-time singular Markov jump systems (SMJSs) with asynchronous switching, which means the switching of controllers is asynchronous with the switching of subsystems. The switching delay and state delay are modeled as Markov chains. The resulting closed-loop system is modeled as a singular system with a Markovian jumping vector and two Markovian jumping parameters. A new necessary and sufficient condition for regularity, causality and stability of the closed-loop system is proposed. Based on this, a state feedback controller is designed in terms of a strict linear matrix inequality (LMI) to guarantee the admissibility of SMJSs with asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Finite-time state estimation for jumping recurrent neural networks with deficient transition probabilities and linear fractional uncertainties

This paper is concerned with the finite-time stability and the finite-time boundedness issues on the estimation problem for a class of continuous-time uncertain recurrent neural networks with Markovian jumping parameters. The uncertain parameters are described by the linear fractional uncertainties and the jumping parameters obey the homogeneous Markov process with possibly deficient probability transition matrix. A full-order state estimator is constructed to estimate the neuron state, in presence of the uncertain and jumping parameters, such that the resulting error dynamics of the state estimation is (i) finite-time stable in the disturbance-free case; and (ii) finite-time bounded in case of exogenous disturbances on the measurements. By employing the Lyapunov stability theory and stochastic analysis techniques, sufficient conditions are established that ensure the existence of the desired finite-time state estimator, and then the explicit expression of such state estimators is characterized in terms of the feasibility to a convex optimization problem that can be easily solved by using the semi-definite programme method. Validity and effectiveness of the developed design method are demonstrated by a numerical example.

Passivity analysis of neural networks with two different Markovian jumping parameters and mixed time delays

This paper studies the problem of passivity analysis for neural networks with two different Markovian jumping parameters and mixed time delays utilizing some integral inequalities. The integral inequalities produce sharper bounds than what the Jensen's inequality produces, consequently, better results are obtained. The Markovian jumping parameters in connection weight matrices and discrete delay are assumed to be different in the system model. By constructing a new appropriate Lyapunov-Krasovskii functional (LKF), some sufficient conditions are established which guarantee the passivity of the proposed model. Numerical examples are given to show the less conservatism and effectiveness of the proposed method.

Robust $$H_\infty$$ H ∞ filtering for uncertain discrete-time stochastic neural networks with Markovian jump and mixed time-delays

In this paper, the robust $$H_\infty$$ filtering problem is discussed for a class of uncertain discrete-time stochastic neural networks with Markovian jumping parameters and mixed time-delays. Norm-bounded parameter uncertainties exist in both the state and measurement equation. The neuron activation function satisfies sector-bounded condition. The aim is to design a full-order filter with a prescribed $$H_\infty$$ performance level. Delay-segment-dependent conditions are developed in terms of linear matrix inequalities (LMIs) such that the resulted filtering error systems robustly stochastically stable. Finally, example is provided to demonstrate the effectiveness and applicability of the related results are obtained in this paper.