Markovian Jumping Parameters Research Articles

State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control

In this paper, we are concerned with the problem of state estimation of Takagi–Sugeno (T–S) fuzzy delayed neural networks with Markovian jumping parameters via sampled-data control. Based on the fuzzy-model-based control approach and linear matrix inequality (LMI) technique, several novel conditions are derived to guarantee the stability of the suggested system. A new class of Lyapunov functional, which contains integral terms, is constructed to derive delay-dependent stability criteria. Some characteristics of the sampling input delay are proposed based on the input delay approach. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

Pinning sampled‐data synchronization of complex dynamical networks with Markovian jumping and mixed delays using multiple integral approach

This study deals with the pinning synchronization problem for complex dynamical networks (CDNs) with Markovian jumping parameters and mixed delays under sampled‐data control technique. The mixed delays cover both discrete and distributed delays. The Markovian jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. The sufficient conditions for asymptotic synchronization of considered networks are obtained by utilizing novel Lyapunov‐Krasovskii functional and multiple integral approach. The obtained criteria is formulated in terms of LMIs, which can be checked for feasibility by making use of available softwares. Lastly, numerical simulation results are presented to validate the advantage of the propound theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 622–632, 2016

Optimal control for a singularly perturbed linear stochastic system with multiplicative white noise perturbations and Markovian jumping

SummaryIn this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations, a parameter‐independent composite controller is derived. Furthermore, the cost degradation in a reduced‐order controller is discussed. Thus, the exactness of the proposed approximate control is discussed for the first time. As an additional important contribution, a numerical algorithm for solving the coupled stochastic algebraic Riccati equations is proposed, and the feature of the resulting higher‐order controller is shown. Finally, a simple example is presented to demonstrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations

In this paper, the finite-time synchronization and identification for the uncertain system parameters and topological structure of complex delayed networks with Markovian jumping parameters and stochastic perturbations is studied. On the strength of finite time stability theorem and appropriate stochastic Lyapunov–Krasovskii functional under the Itô’s formula, some sufficient conditions are obtained to assurance that the complex delayed networks with Markovian switching dynamic behavior can be identified the uncertain parameters and topological structure matrix in finite time under stochastic perturbations. In addition, three numerical simulations of different situation and dimension are presented to illustrate the effectiveness and feasibility of the theoretical results.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

AbstractThis article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

Non-fragile state estimation for discrete Markovian jumping neural networks

In this paper, the non-fragile state estimation problem is investigated for a class of discrete-time neural networks subject to Markovian jumping parameters and time delays. In terms of a Markov chain, the mode switching phenomenon at different times is considered in both the parameters and the discrete delays of the neural networks. To account for the possible gain variations occurring in the implementation, the gain of the estimator is assumed to be perturbed by multiplicative norm-bounded uncertainties. We aim to design a non-fragile state estimator such that, in the presence of all admissible gain variations, the estimation error converges to zero exponentially. By adopting the Lyapunov–Krasovskii functional and the stochastic analysis theory, sufficient conditions are established to ensure the existence of the desired state estimator that guarantees the stability of the overall estimation error dynamics. The explicit expression of such estimators is parameterized by solving a convex optimization problem via the semi-definite programming method. A numerical simulation example is provided to verify the usefulness of the proposed methods.

Consensus in second‐order Markovian jump multi‐agent systems via impulsive control using sampled information with heterogenous delays

AbstractThis paper investigates the consensus problem of second‐order Markovian jump multi‐agent systems with delays. Both network‐induced random delay and node‐induced state delay are considered, where the network‐induced random delay, subjected to a Markov chain, exists in the switching signal and the node‐induced state delay, related to switching topologies, is heterogeneous between any two linked agents. In order to reduce communication and control energy, an impulsive protocol is proposed, where each agent only can get delayed relative positions to neighbors and the velocity of itself at impulsive instants. By performing three steps of model transformation and introducing a mapping for two independent Markov chains, the consensus problem of the original continuous‐time system is equivalent to the stability problem of a discrete‐time expand error system with two Markovian jumping parameters and a necessary and sufficient criterion is derived. A numerical example is given to illustrate the effectiveness of the theoretical result.@@@@This work is supported by the National Natural Science Foundation of China under Grants 61374171, 61572210, and 51537003, the Fundamental Research Funds for the Central Universities (2015TS030), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245).

Exponential passivity analysis of stochastic neural networks with leakage, distributed delays and Markovian jumping parameters

This paper deals with the problem of exponential passivity of Markovian jumping stochastic neural networks with leakage and distributed delays. By constructing a proper Lyapunov–Krasovskii functional, utilizing the free-weighting matrix method and some stochastic analysis techniques, we deduce new delay-dependent sufficient conditions that ensure the passivity of the proposed model. These sufficient conditions are computationally efficient and they can be solved numerically by linear matrix inequality (LMI) toolbox in Matlab. Finally, numerical examples are given to verify the effectiveness and the applicability of the proposed results.

Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction---diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction---diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov---Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results.

Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays

In this paper, the event-triggered H∞ state estimation problem is investigated for a class of discrete-time stochastic genetic regulatory networks with both Markovian jumping parameters and time-varying delays. The jumping parameters are governed by a homogeneous Markovian chain and the time-varying delays under consideration occur in both the feedback regulatory process and transcription process. The aim of this paper is to estimate the concentrations of mRNA and protein in such genetic regulatory networks by using the available measurement outputs. In order to reduce the information communication burden, the event-triggered mechanism is adopted and the measurement outputs are only transmitted to the estimator when a certain triggered condition is met. By constructing an appropriate Lyapunov functional, some sufficient conditions are derived under which the estimation error dynamics is stochastically stable and the H∞ performance constraint is satisfied. Based on the analysis results, the desired H∞ estimator parameters are designed in terms of the solution to a set of matrix inequalities that can be easily solved by the Matlab toolboxes. Finally, a simulation example is provided to illustrate the effectiveness of the proposed event-triggered state estimation scheme.

Passivity analysis of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters

This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. 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.

Almost sure [formula omitted] filtering for nonlinear hybrid stochastic systems with mode-dependent interval delays

In this paper, the problem of almost sure H∞ filtering is studied for a class of nonlinear hybrid stochastic systems. In the system under investigation, Markovian jumping parameters, mode-dependent interval delays, nonzero exogenous disturbances as well as white noises are simultaneously taken into consideration to better model the real-world systems. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the almost surely exponential stability and the prescribed H∞ performance for the overall filtering error dynamics. Furthermore, the obtained results are applied to two classes of special hybrid stochastic systems with mode-dependent interval delays, where the desired filter gain is obtained in terms of the solutions to a set of linear matrix inequalities. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design scheme.

Adaptive estimation for delayed neural networks with Markovian jumping parameters

In this letter, the adaptive estimation problem of the neuron states is studied for delayed neural networks with Markovian jumping parameters. Through employing a new nonnegative function and the M-matrix method, some sufficient conditions are derived to ensure the almost sure asymptotical stability for the dynamics of estimator error. Several suitable parameters update laws are found by the adaptive feedback control technique. Finally, a simulation example is provided to illustrate the effectiveness of the proposed adaptive estimation method.

Stochastic stability of uncertain recurrent neural networks with Markovian jumping parameters

In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequality(LMI) based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters.The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.

Synchronization of Markovian jumping complex networks with event-triggered control**Project supported by the National Natural Science Foundation of China (Grant No. 11202084).

This paper investigates event-triggered synchronization for complex networks with Markovian jumping parameters. Nonlinear dynamics with Markovian jumping parameters is considered for each node in a complex network. By utilizing the proposed event-triggered strategy, and based on the Lyapunov functional method and linear matrix inequality technology, some sufficient conditions for synchronization of complex networks are derived whether the transition rate matrix for the Markov process is completely known or not. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.

Stochastic stability for discrete‐time antilinear systems with Markovian jumping parameters

In this study, the discrete-time antilinear systems with Markovian jumping parameters are investigated. The concept of stochastic stability is extended to the context of discrete-time Markovian jump (DTMJ) antilinear systems. By using stochastic Lyapunov approach, the authors derive some necessary and sufficient conditions for a DTMJ antilinear system to be stochastically stable in terms of coupled anti-Lyapunov matrix equations. In addition, two types of iterative algorithms are proposed to solve these coupled anti-Lyapunov matrix equations. Finally, some numerical examples are given to show the efficiency of the proposed algorithms and potential applications of the obtained results on antilinear systems.

State estimation for uncertain discrete-time stochastic neural networks with Markovian jump parameters and time-varying delays

The state estimation problem is considered for a class of discrete-time stochastic neural networks with Markovian jumping parameters in this paper. Norm-bounded parameter uncertainties in the state and measurement equation and time-varying delays are investigated. The neuron activation function satisfies sector-bounded conditions, and the nonlinear perturbation of the measurement equation satisfies standard Lipschitz condition and sector-bounded conditions. By constructing proper Lyapunov–Krasovskii functional, delay-dependent conditions are developed in terms of linear matrix inequalities (LMIs) to estimate the neuron state such that the dynamic of the estimation error system is asymptotically stable. Finally, numerical examples are shown to demonstrate the effectiveness and applicability of the proposed design method.

New delay‐dependent global robust passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays

The problem of passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays is investigated in this article. By constructing a novel Lyapunov–Krasovskii functional based on the complete delay‐decomposing idea and using improved free‐weighting matrix method, some improved delay‐dependent passivity criteria are established in terms of linear matrix inequalities. Numerical examples are also given to show the effectiveness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 167–179, 2016

H∞ sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters

This paper is devoted to the investigation of H ∞ sliding mode control (SMC) for uncertain neutral stochastic systems with Markovian jumping parameters and time-varying delays. A sliding surface functional is firstly constructed. Then, the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite-time interval. The sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the efficiency of the proposed method.

Mode and Delay-dependent Stochastic Stability Conditions of Fuzzy Neural Networks with Markovian Jump Parameters

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square. By using the reciprocal convex combination approach, Jensen and Jensen-type integral inequality, linear convex combination technique and the free-weight matrix method, several novel mode and delay-dependent sufficient conditions are derived to ensure the stochastic stability of the equilibrium point of the considered networks in mean square. The proposed results can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.