Markovian Jumping Parameters Research Articles

H∞ mode-independent filter design for Markovian jump genetic regulatory networks with time-varying delays

This paper investigates the problem of designing H∞ filter for gene regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. Since in real gene networks the current jump mode is not easily accessible, the filter parameters are considered to be independent from the current system mode. By using mode-dependent Lyapunov–Krasovski functionals, appropriate conditions for the stochastic stability and disturbance attenuation of mixed GRN/filter system is derived. Mode independent filter gains are then obtained from some sufficient conditions in the form of linear matrix inequalities which are easy to solve by numerical methods. In the end, a numerical example and the relevant simulations are presented to evaluate the results.

Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters

This paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear first-order hyperbolic partial differential equations (FOHPDEs) with Markov jumping parameters, for which the manipulated input is distributed in space. Based on an integral-type stochastic Lyapunov functional (ISLF), the sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of spatial differential linear matrix inequalities (SDLMIs). Then, an SDLMI approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition. Furthermore, using the finite difference method and the standard linear matrix inequality (LMI) optimization techniques, recursive LMI algorithms for solving the SDLMIs in the analysis and synthesis are provided. Finally, a simulation example is given to demonstrate the effectiveness of the developed design method.

New robust passivity criteria for discrete-time genetic regulatory networks with Markovian jumping parameters

In this paper, we present some novel results for robust passivity of a class of uncertain discrete-time Markovian jumping genetic regulatory networks (GRNs) with time-varying delays. By constructing a new set of Lyapunov–Krasovskii functionals, together with the matrix inequality technique, we provide a new set of results for the passiveness, and also ensure the mean-square asymptotical stability (internally) of the considered GRNs about their equilibrium points for all time delays satisfying both the lower bound and upper bound of the interval time-varying delay. Further, the obtained results are extended to deal with the robust passiveness of the considered GRNs for all admissible uncertainties. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, numerical examples with simulation results are provided for the GRN model to illustrate the applicability and usefulness of the theory.

Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays

This paper deals with the problem of stability analysis of non-linear singular systems with Markovian jumping parameters and mode-dependent interval time varying delays. New delay-dependent stability conditions are derived in terms of linear matrix inequalities (LMIs) by constructing a mode-dependent Lyapunov–Krasovskii functional and using some integral inequalities. Numerical examples are presented to illustrate the usefulness and less conservativeness of the proposed theoretical results.

Delay‐Dependent Exponential Stability for Uncertain Neutral Stochastic Systems with Mixed Delays and Markovian Jumping Parameters

This paper is mainly concerned with the globally exponential stability in mean square of uncertain neutral stochastic systems with mixed delays and Markovian jumping parameters. The mixed delays are comprised of the discrete interval time‐varying delays and the distributed time delays. Taking the stochastic perturbation and Markovian jumping parameters into account, some delay‐dependent sufficient conditions for the globally exponential stability in mean square of such systems can be obtained by constructing an appropriate Lyapunov‐Krasovskii functional, which are given in the form of linear matrix inequalities (LMIs). The derived criteria are dependent on the upper bound and the lower bound of the time‐varying delay and the distributed delay and are therefore less conservative. Two numerical examples are given to illustrate the effectiveness and applicability of our obtained results.

Robust l2–l∞ Filtering for Discrete-Time Systems with Markovian Switching and Mode-Dependent Time-Delays

This paper is concerned with the problem of robust l2–l∞ filtering for a class of discrete-time linear uncertain systems with Markovian jumping parameters and mode-dependent time-delays. The uncertainties are assumed to be time-varying but norm-bounded. Attention is focused on the design a full-order Markovian jump linear filter that ensures stochastically stability and guarantees a prescribed energy-to-peak disturbance attenuation level for the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrices. Sufficient conditions for the solvability of the problem are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed techniques.

Mean Field Games for Large-Population Multiagent Systems with Markov Jump Parameters

In this paper, distributed games for large-population multiagent systems with random time-varying parameters are investigated, where the agents are coupled via their individual costs and the structure parameters are a family of independent Markov chains with identical generators. The cost function of each agent is a long-run average tracking-type functional with an unknown mean field coupling nonlinear term as “reference signal.” To reduce the computational complexity, the mean field approach is applied to construct distributed strategies. The population statistics effect (PSE) is used to approximate the average effect of all the agents, and the distributed strategies are given through solving a Markov jump tracking problem. Here the PSE is a deterministic quantity and can be obtained by solving the Stackelberg equilibrium of an auxiliary two-player game. It is shown that the closed-loop system is uniformly stable, and the distributed strategies are asymptotically optimal in the sense of Nash equilibrium,...

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

In this paper, a sliding-mode approach is proposed for exponential H∞ synchronization problem of a class of master–slave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov–Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law, which include the master–slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H∞ synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.

Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters: A delay decomposition approach

Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters: A delay decomposition approach

Delay-dependent global asymptotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters

This paper investigates the delay-dependent global asymptotic stability problem of stochastic genetic regulatory networks (SGRNs) with Markovian jumping parameters. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, a delay-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are globally asymptotically stable in the mean square. Distinct difference from other analytical approaches lies in “linearization” of the genetic regulatory networks (GRNs) model, by which the considered GRN model is transformed into a linear system. Then, a process, which is called parameterized first-order model transformation is used to transform the linear system. Novel criteria for global asymptotic stability of the SGRNs with constant delays are obtained. Some numerical examples are given to illustrate the effectiveness of our theoretical results.

Exponential stability of stochastic reaction–diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters

In this paper, we investigate the robust exponential stability for stochastic reaction–diffusion uncertain fuzzy neural networks with mixed delays and Markovian jump parameters. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain sufficient conditions for the exponential stability of the equilibrium solution. The obtained stability criteria can be easily checked by linear matrix inequality (LMI) techniques. Finally numerical examples are provided to illustrate the obtained theoretical result.

Stability analysis for discrete delayed Markovian jumping neural networks with partly unknown transition probabilities

This paper addresses the analysis problem of asymptotic stability for a class of uncertain neural networks with Markovian jumping parameters and time delays. The considered transition probabilities are assumed to be partially unknown. The parameter uncertainties are considered to be norm-bounded. A sufficient condition for the stability of the addressed neural networks is derived, which is expressed in terms of a set of linear matrix inequalities. A numerical example is given to verify the effectiveness of the developed results.

Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays

In this paper, passivity analysis is conducted for discrete-time stochastic neural networks with both Markovian jumping parameters and mixed time delays. The mixed time delays consist of both discrete and distributed delays. The Markov chain in the underlying neural networks is finite piecewise homogeneous. By introducing a Lyapunov functional that accounts for the mixed time delays, a delay-dependent passivity condition is derived in terms of the linear matrix inequality approach. The case of Markov chain with partially unknown transition probabilities is also considered. All the results presented depend upon not only discrete delay but also distributed delay. A numerical example is included to demonstrate the effectiveness of the proposed methods.

State Estimation for Discrete-Time Singular Jump Systems with Non-Accessible Mode Information

The mode information of Markovian jumping systems is always not accessible due to unexpected phenomenon such as data packet losses in networked control systems. It is thus extremely desirable to develop mode-independent filtering techniques for Markovian jumping systems. In this paper, a new mode-independent filtering design strategy is presented for a class of discrete-time singular time-delay systems with Markovian jumping parameters. Sufficient conditions are established so that the derived error system is regular, causal and stochastically stable with a prescribed H∞ performance level. In addition, it is illustrated that the proposed results are less conservative numerically than those in the references. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed approaches.

New results of robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters1The work of authors was supported by Department of Science and Technology, New Delhi, India, under the sanctioned No. SR/S4/MS:485/07.

In this paper, robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters is conducted. By using the delay-decomposition approach, a new Lyapunov–Krasovskii functional is constructed. Based on this Lyapunov–Krasovskii functional and some stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the effectiveness and reduced conservatism of our theoretical results.

Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses

In this paper, the problem of neutral-type impulsive bidirectional associative memory neural networks (NIBAMNNs) with time delays are first established by a Takagi–Sugeno (T-S) fuzzy model in which the consequent parts are composed of a set of NIBAMNNs with interval delays and Markovian jumping parameters (MJPs). Sufficient conditions to check the robust exponential stability of the derived model are based on the Lyapunov–Krasovskii functionals (LKFs) containing some novel triple integral terms, Lyapunov stability theory and employing the free-weighting matrix method. The delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs), which can be very efficiently solved using Matlab LMI control toolbox. Finally, numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results.

Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters

This paper deals with the global exponential stability in the mean square of fuzzy cellular neural networks with time-varying delays and Markovian jumping parameters. By constructing suitable Lyapunov functionals, we obtain several sufficient conditions which can be expressed in terms of linear matrix inequalities (LMIs). The proposed LMI results are computationally efficient as it can be solved numerically by using Matlab LMI toolbox. An example is given to show the effectiveness of the results.

Time‐delay dependent H∞ model simplification for singular systems with Markovian jumping parameters

AbstractThe problem of H∞ model simplification for singular systems with Markovian jumping parameters and time‐delay is investigated. For a given stochastic stable system, our attention is focused on the construction of reduced‐order models which guarantee the corresponding error system to be admissible and have a prescribed H∞ error performance. A robust admissibility condition and a robust bounded real lemma are developed based on which, sufficient conditions for the existence of desired reduced‐order models are proposed. Desired reduced‐order model can be constructed when the proposed conditions are satisfied. The effectiveness of the proposed model reduction method is illustrated via a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.

DYNAMICS ANALYSIS OF IMPULSIVE STOCHASTIC HIGH-ORDER BAM NEURAL NETWORKS WITH MARKOVIAN JUMPING AND MIXED DELAYS

This paper deals with the problem of asymptotical stability in mean square for a class of impulsive stochastic high-order bi-directional associative memory (BAM) neural networks with mixed delays and Markovian jumping parameters. Based on Lyapunov stability theory, linear matrix inequality and mathematical induction, some sufficient conditions are derived for the asymptotical stability in mean square of the equilibrium point of the neural networks. The results obtained in this paper are new and complement previously known results.

Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays

In this paper, the problem of robust exponential stability analysis of uncertain discrete-time recurrent neural networks with Markovian jumping and time-varying delays is studied. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient criterion is proposed for the global robust exponential stability of discrete-time recurrent neural networks which contain uncertain parameters and Markovian jumping parameters. The obtained stability criterion is characterized in terms of linear matrix inequalities (LMIs) and can be easily checked by utilizing the efficient LMI toolbox. Two numerical examples are presented to show the effectiveness and conservativeness of the proposed method.