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This brief discusses $p$ th moment exponential synchronization of multi-agent systems (MASs). First, a new model is proposed, which includes Lévy noise and Markov switching. Second, based on Lyapunov stability theory, the exponential stability criterion for one-leader multi-follower MASs is obtained. At the same time, leaderless multi-agent systems (LMASs) are constructed, which are different from leader-follower MASs. LMASs have no signal guidance and rely only on information transmission from neighbors. Compared with some existing results, the controller without signed functional is proposed to achieve $p$ th moment exponential synchronization of MASs, which avoids chattering phenomenon. Finally, simulation verifies the validity of these conclusions.

In this letter, the problem of false data injection (FDI) attacks is investigated for dc microgrid systems, which involves Markovian jumping parameters and Lévy noises. Moreover, an adaptive sliding mode controller is constructed to assure the stability of such dc microgrid systems. First, the dynamical equations of dc microgrid systems are proposed, which consider Lévy noises and Markovian jumping parameters. Meanwhile, the impact of FDI attacks is taken into account in dc microgrid systems. Next, the sliding mode motion dynamic of dc microgrid systems can be attained by designing a sliding mode surface (SMS) in the form of integral. Several sufficient conditions are proposed to guarantee the asymptotic stability for dc microgrid systems. Then, a novel sliding mode control (SMC) law is put forward to drive systems to reach and maintain a given sliding mode surface. In addition, the solution of linear matrix inequalities can determine undetermined parameters in the SMC and SMS. Ultimately, a practical example is demonstrated to prove that the proposed adaptive sliding mode controller can ensure the stability of the dc microgrid system under FDI attacks.

Prescribed-time consensus tracking for second-order nonlinear multiagent systems (MASs) with the unknown nonlinear dynamics satisfying a time-varying Lipschitz growth rate is investigated in this article. A time-varying function is introduced as a part of the controller gains, and it plays an important role in overcoming the rapid growth of nonlinear terms and in ensuring that the consensus can be achieved in a preassigned time. An integral sliding-mode control protocol, which forces the system trajectory to move on to the defined sliding manifold at the initial moment, is proposed for solving the prescribed-time consensus tracking problem of leader-following MASs with disturbances. Furthermore, we propose a slightly different control law based on terminal sliding-mode control, and under such a controller, the trajectories of each follower reach the sliding manifold in an arbitrary assigned time $T_{1}$ , and then in a specified time $T_{2}$ , the position and velocity tracking errors for all followers converge to 0 at the same time instant. Based on the graph theory, state transformations, and Lyapunov theorem, we prove that the proposed solutions are feasible and, finally, three simulation examples are provided to verify the theoretical results.

The fixed-time synchronization and energy consumption of Kuramoto-oscillator networks with multilayer distributed control are studied in this brief. In order to achieve fixed-time synchronization, multilayer networks are designed, including the proportional layer, the finite-time layer and the fixed-time layer. Then, to overcome that Kuramoto-oscillator networks cannot realize synchronization at the desired time, the sufficient conditions for Kuramoto-oscillator networks are proposed to guarantee the fixed-time synchronization. To achieve energy saving of the controller, the supremum of energy consumption is obtained when the Kuramoto-oscillator networks reach synchronization. Finally, an example for Kuramoto-oscillator networks is given to illustrate the effectiveness of the proposed synchronization and energy consumption.

This article focuses on the finite-time and prescribed-time cluster synchronization problems of switched complex networks with proportional delays. Considering that the matched controller often switches behind the switched systems, asynchronous switching law and switching parameters have been introduced to the complex dynamical networks. By applying the stability theory of dynamical systems and the average dwell time approach, some sufficient criteria in form of linear matrix inequalities have been developed to guarantee such networks finite/prescribed-time cluster synchronization under the pinning control scheme. Finally, one numerical example is presented to show the effectiveness of the theoretical results.

Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example. [ABSTRACT FROM AUTHOR]

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This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert–Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques. [ABSTRACT FROM PUBLISHER]

In proportional-integral-derivative (PID) controller design, obtaining high stability and desired closed-loop response are of great importance for system engineers. Most existing methodologies, which have validated their excellent control performance on the accurate mathematical model, face significant difficulties in the unavoidable model mismatches and disturbance. To overcome these drawbacks, this paper proposes a self-adaptive state-space predictive functional control (APFC) based on extremal optimization method to design PID controller called EO-APFC-PID, wherein, the self-adaptive means, i.e., a forgetting factor recursive least squares (FFRLS) mechanism is embedded into state-space predictive functional control (PFC), and the proposed EO is exploited to alleviate the challenging problem that the elements in weighting factors of APFC technique are lacking analytical knowledge. The performance of the proposed EO-APFC-PID control scheme is demonstrated and compared with one classic PID tuning method and two state-of-the-art control strategies on the chamber pressure control for a coke furnace. The experimental results fully illustrate that the proposed method is more effective and efficient than other existing control strategies for achieving a desired behavior on the most test cases considered in this paper in terms of set point tracking, input disturbance rejection and output disturbance rejection. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of adaptive exponential synchronization in mean square for a new neural network model with the following features: 1) the noise is characterized by the Lévy process and the parameters of the model change in line with the Markovian process; 2) the master system is also disturbed by the same Lévy noise; and 3) there are multiple slave systems, and the state matrix of each slave system is an affine function of the state matrices of all slave systems. Based on the Lyapunov functional theory, the generalized Itô’s formula, $M$ -matrix method, and the adaptive control technique, some criteria are established to ensure the adaptive exponential synchronization in the mean square of the master system and each slave system. Moreover, the update law of the control gain and the dynamic variation of the parameters of the slave systems are provided. Finally, the effectiveness of the synchronization criteria proposed in this paper is verified by a practical example.

This paper discusses the problem of optimal control and nonzero-sum game for stochastic differential system with Lévy noise and Markovian switching parameters. Based on Bellman’s principle of dynamic programming and Dynkin’s formula, a generalized Hamiltonian-Jacobi-Bellman (HJB) equation is given for solving stochastic differential games. Specifically, for a linear quadratic Gaussian nonzero-sum game with Lévy noise and Markovian switching parameters, the Nash equilibrium strategy is obtained by using this generalized HJB equation. Finally, an example of stock investment strategy optimization in financial market game is provided as an application.

In this paper, we investigate the exponential synchronization problem for a new class of stochastic neural networks driven by fractional Brownian motion (fBm). In order to deal with the problem of stability for the error system, we propose the mild solution of system equation with respect to fractional Brownian motion based on the space of Hilbert–Schmidt operator law. By using the infinitesimal generator on analytic semigroup principle and associating with the well-known Hölder inequality, Gronwall inequality, we obtain the exponential synchronization criteria for the drive system and response system driven by fBm. Finally, two numerical examples as well as some evolution figures are implemented to demonstrate the effectiveness and feasibility of the proposed exponential synchronization schemes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the adaptive exponential synchronization problem for stochastic neural networks with multi-delayed and Markovian switching. A new method called M -matrix method, very different to the linear matrix inequality (LMI) method, has been proposed to solve the above problem. Meanwhile, some sufficient conditions for the exponential stability of the error system are derived. The feedback gain update laws are given by the adaptive control technique. Finally, two simulation examples are provided to demonstrate the effectiveness and applicability of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper addresses the stochastic synchronization problem for a class of neural networks with multiple time-varying delays and Markovian jump. By choosing a non-negative function, M-matrix technique and stochastic analysis approach, several sufficient conditions are obtained to guarantee that the error system is stable. Moreover, the update laws of the gain matrix are derived to ensure stochastic synchronization for multiple time-varying delayed drive system and response system. In particular, the M-matrix associates with the Markovian chain generated by transmission rate matrix. And the condition of M-matrix can be verified conveniently in practice. In the end, the effectiveness and potential value of the results addressed are tested by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the robust synchronization problem for a class of stochastic delayed complex networks with switching topology and unmodeled dynamics is investigated by using the adaptive control scheme. Different from some existing uncertain complex network models, the uncertain terms in the complex networks are only needed to be bounded. Based on the stability theory of stochastic delayed differential equation, a novel adaptive controller which ensures that all the nodes in the complex networks robustly synchronize with the target node is derived. Finally, a numerical example is provided to show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: Based on the conflict and crosstalk avoidance mechanism (CCAM), we propose a sleeping–awaking method for wireless sensor networks (WSNs) in which the maximal degree node (MDN) and all its neighbors run sleep or wake simultaneously while other nodes run the CCAM. This method is said to be the same sleeping–awaking method (SSAM). The SSAM is motivated by the congestion and collision problems of cliques, MDN and its neighbor set in the communicating graph of the WSN. In this communication way, the related protocol about the SSAM is provided accordingly. Under the designed protocol, we get a Markovian switching WSN with both white noise disturbance and multiple time-varying delays. Based on the theory of exponential stability in pth moment, we show that the protocol ensures the WSNs to keep in synchronization with the target function. A numerical example shows that the WSN can keep its target-synchronization even with large time delays. [Copyright &y& Elsevier]

Abstract: The synchronization control problem for the competitive complex network with time delay and stochastic effects is investigated by using the stochastic technique and Lyapunov stability theory. The competitive complex network means that the dynamical varying rate of a part of nodes is faster than other nodes. Some synchronization criteria are derived by the full controller and pinning controller, respectively, and these criteria are convenient to be used for concision. A numerical example is provided to illustrate the effectiveness of the method proposed in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of the mean square exponential synchronization in Lagrange sense for the uncertain complex network is investigated. A complex network usually appears some uncertain phenomena, which includes varying topology structure, destroyed nodes, and the noise disturbance from circumstance. Based on the Lyapunov stability theory and the Kronecker product analysis technique, some conditions to guarantee the complex network mean square exponential synchronization in Lagrange sense are provided. Finally, two numerical examples are provided to illustrate the effectiveness of the method proposed. [Copyright &y& Elsevier]

In this brief, the analysis problem of the mode and delay-dependent adaptive exponential synchronization in th moment is considered for stochastic delayed neural networks with Markovian switching. By utilizing a new nonnegative function and the -matrix approach, several sufficient conditions to ensure the mode and delay-dependent adaptive exponential synchronization in th moment for stochastic delayed neural networks are derived. Via the adaptive feedback control techniques, some suitable parameters update laws are found. To illustrate the effectiveness of the -matrix-based synchronization conditions derived in this brief, a numerical example is provided finally.

A new chaotic system is found by feedback controlling method in this paper. According to the definition of the generalized Lorenz system, the new chaotic system does not belong to generalized Lorenz systems. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map. The particular interest is that this novel system can generate two one‐scroll and one two‐scroll chaotic attractors with the variation of a single parameter. The obtained results show clearly that the system is a new chaotic system and deserves a further detailed investigation. Copyright © 2011 John Wiley & Sons, Ltd.

Abstract: The problem of adaptive synchronization for the uncertain chaotic systems with adaptive scaling function is investigated in this paper. In comparison to those of the existing scaling function synchronization, such as the presetting scaling function, the aim of this paper is focused not only on the scaling function but also on the identification of parameters of the chaotic system. Finally, to illustrate the implementation of the proposed method, some numerical simulations are given. [Copyright &y& Elsevier]

Abstract: This paper discusses topology identification and adaptive synchronization of uncertain complex networks with adaptive the scaling functions. In comparison with those of the existing scaling function synchronization, the scaling function can be identified by adaptive laws in this paper. Moreover, the uncertain network topological structure are identified simultaneously in the process of synchronization. Illustrative examples are presented to demonstrate the application of the theoretical results. [Copyright &y& Elsevier]

Abstract: This work investigates chaos synchronization between two different fractional-order hyperchaotic system (FOHS)s. A novel FOHS is also proposed in this paper. The Chen FOHS is controlled to be a new FOHS and the Lü FOHS, respectively. The analytical conditions for the synchronization of these pairs of different FOHSs are derived by utilizing Laplace transform. Furthermore, synchronization between two different FOHSs is achieved by utilizing feedback control method in a quite short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses the synchronization and anti-synchronization of new uncertain fractional-order unified chaotic systems (UFOUCS). Based on the idea of active control, a novel active pinning control strategy is presented, which only needs a state of new UFOUCS. The proposed controller can achieve synchronization between a response system and a drive system, and ensure the synchronized robust stability of new UFOUCS. Numerical simulations of new UFOUCS show that the controller can make fractional-order unified chaotic systems (FOUCS) achieve synchronization or anti-synchronization in a quite short period and both are of good robust stability. [Copyright &y& Elsevier]

Abstract: This paper proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks with non-derivative and derivative coupling. By designing effective adaptive controller, the unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results obtained in this paper. [Copyright &y& Elsevier]

Abstract: This paper reports a novel chaotic member to the three-dimensional smooth autonomous quadratic system family, which is derived from the classical Chen system but exhibits a three-scroll chaotic attractor. The basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincaré map and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. Simulation results clearly show that this is a novel chaotic system and deserves further detailed investigation. [Copyright &y& Elsevier]

Abstract: This paper introduces a modified Lü chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lü chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods. [Copyright &y& Elsevier]

This paper focuses on the problem of hybrid-driven-based H ∞ filtering design for networked systems under randomly occurring deception attacks (RODAs). To reduce the burden on the network, a hybrid trigger mechanism consisting of time-triggered mechanism (TTM) and event-triggered mechanism (ETM) has been introduced. By introducing random variables that satisfy a 0–1 distribution, the switching law of two different deception attacks is described and a mathematical model of RODAs is developed. Furthermore, a filtering error model is constructed. Then, sufficient conditions for the stability of the proposed filter system are obtained using the Lyapunov–Krasovskii functional (LKF) and linear matrix inequalities (LMIs) techniques, and the parameters of the designed filter are given in an explicit form. We use Jensen's Inequality to estimate quadratic integral terms and the reciprocally convex combination lemma (RCCL) to deal with time delay-dependent integral terms. Finally, the feasibility of the method is verified by numerical examples. [ABSTRACT FROM AUTHOR]

The finite-time stochastic boundedness (FTSB) via the sliding mode control (SMC) approach is analyzed for Markovian jumping systems (MJSs) with time-delays. First, an integral switching surface is constructed. And to make sure the reachability of the sliding mode surface in a finite-time, an SMC law is designed. In addition, the delay-dependent criteria for FTSB are obtained over the reaching phase and the sliding motion phase. Furthermore, in line with linear matrix inequalities (LMIs), sufficient conditions are provided to guarantee the FTSB of systems over the whole finite-time interval. Lastly, an example is given to indicate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered control for the class of Markovian jump neural networks (MJNNs) under actuator saturation and hybrid cyber attacks. In order to save the limited network bandwidth, the event-triggered mechanism (ETM) is introduce to determine whether the signal of sampler is transmitted to the remote controller through the communication network. With the aid of two sets of Bernoulli distributed random variables (BDRVs), the mathematical model of randomly occurring deception attacks (RODAs) is presented. Due to the limitations of security and technology factors and the complex network environment in practice, actuator saturation and denial-of-service (DoS) attack are also considered. In summary, the MJNNs, ETM, actuator saturation and hybrid cyber attacks are incorporated into a unified construction, and a augmented system under this construction is modeled for the first time. For this system, the existence conditions of event-triggered control are derived through LyapunovKrasovskii functional (LKF). Based on this sufficient condition, the linear matrix inequality (LMI) technique is utilized to obtain the control gain of the controller and the weight matrix of the trigger. Finally, a numerical example is given to verify the effectiveness of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

This paper is studied with the hierarchical type stability and stabilization of networked control systems (NCSs) with event-triggered mechanism (ETM). In the cause of reducing the amount of data transmission and saving the limited network bandwidth, ETM is introduced into NCSs, and the closed-loop time-delay NCSs model with ETM is presented. An improved Lyapunov–Krasovskii functional (LKF), containing delay-product-type terms and being appropriate for the canonical BesselLegendre inequality (BLI), is first constructed. Then, by utilizing the canonical BLI and the extended reciprocally convex matrix inequality (ERCMI) to deal with the single integral terms of the derivative of LKF, a sufficient condition on asymptotically stable is derived for NCSs. Based on above N-dependent stability criteria, a co-design method is developed, which can be capable of calculating the control gain of controller and the weighting matrix of the ETM. Finally, the feasibility and superiority of the results are verified by two examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability analysis and stabilization problem for a class of uncertain switched delay systems with Lévy noise and flexible switching signals which unify the high-frequency switching and low-frequency switching. By employing the theory of switched systems, mathematical induction and stochastic analysis technique, some sufficient conditions in form of algebraic inequalities are derived to guarantee the stability and stabilization of such systems. Different from dwell time and average dwell time, the proposed switching rule constrained the partial dwell-time shows that the switching number in the same time interval can be more elastic. Finally, numerical examples are implemented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an efficient inverse kinematics (IK) approach which features fast computing performance for a PUMA560-structured robot manipulator. By properties of the orthogonal matrix and block matrix, the complex IK matrix equations are transformed into eight pure algebraic equations that contain the six unknown joint angle variables, which makes the solving compact without computing the reverses of the 4×4 homogeneous transformation matrices. Moreover, the appropriate combination of related equations ensures that the solutions are free of extraneous roots in the solving process, and the wrist singularity problem of the robot is also addressed. Finally, a case study is given to show the effectiveness of the proposed algorithm.

In this paper, the H ∞ synchronization problem of semi-Markovian jump neural networks (s-MJNNs) based on adaptive event-triggered scheme (AETS) output feedback control is studied. Also, the time-varying delay and leakage delay are considered in the system model. In order to solve the problems that the state of the system is not completely observable and limited network resources, an output feedback controller with AETS is designed. At the same time, in order to describe the performance of the sensor in the feedback link, the random nonlinear phenomenon of the sensor is described by the variable complying with Bernoulli probability distribution. A suitable Lyapunov–Krasovskii functional (LKF) is constructed and the bounds of integral terms are estimated by affine Bessel–Legendre inequality. Finally, sufficient conditions for asymptotic stability of the synchronization error system are obtained. And, two numerical examples show the feasibility of the research work. [ABSTRACT FROM AUTHOR]

Abstract: We slightly modify definition in paper [Xu Y, Zhou W, Fang J, Sun W. Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions. Commun Nonlinear Sci Numer Simulat 2011;16:3337–3343], so remark stated problem is resolved in paper . Finally, a more general theorem is given. [Copyright &y& Elsevier]

Abstract: We indicate that the proof of theorem is incorrect in paper [Y. Xu, W. Zhou, J. Fang, W. Sun, Lin Pan, Journal of the Franklin Institute 347 (2010) 1566]. For correcting the mistakes, a correct version of the proof of theorem is given in this paper. [Copyright &y& Elsevier]

In this paper, we investigated the stability of continuous-time nonlinear systems and designed a Neural-Network-Controller based event-triggered. First, we designed a system delay model for the transmission time-delay contained in the system. Based on the designed time-delay model, the input delay method was used to convert the synchronous controller solution problem into a stability problem for the corresponding time-delay system. Second, by using a piecewise Lyapunov-Krasovskii functional combined with the Jensen's inequality, both the stability condition of the continuous-time nonlinear systems and the solution method of sampling controller were given. The designed sampling controller is able to update the control parameters only when the triggering rules are fulfilled, thus reducing the transmission rate of the network. Finally, the effectiveness of the proposed method was verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper discusses the cluster synchronization problem for a class of complex dynamical networks with coupling time delays. Under the randomly occurring coupling time delays condition, a novel complex network model is established to express the dynamical behavior of the nodes more precisely. An improved event-triggered mechanism is proposed for two purpose containing the reduction of network burden and improvement of cluster synchronization efficiency. The pinning control strategy is adopted for cluster synchronization via controlling a small fraction of the network nodes. By employing Lyapunov–Krasovskii functional method, a stability criterion is obtained to ensure the achievement of cluster synchronization and a event-triggered pinning controller is constructed. Finally, a simulation example is expressed to verify the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

This paper discusses the sliding mode control (SMC) problem for nonlinear systems (NSs) with time-varying delays and external disturbances. Different from some existing results, the derivative of the time-varying delay is allowed to be bounded by an arbitrary bounded real number rather than by one. On this basis, an integral sliding mode surface (SMS) with time-varying delays is introduced. By exploiting the Lyapunov stability theory and the improved reciprocally convex inequality, several conditions of globally asymptotically stable are obtained for the sliding mode motion dynamics. Moreover, some results of globally exponentially stable are also established by resorting to double-integral calculations, the integral mean-value theorem and the zero-point existence theorem. Then, the normal/adaptive SMC laws are provided to ensure the reachability of the specified SMS. Finally, the validity and the application of the proposed SMC method are illustrated by two practical examples. [ABSTRACT FROM AUTHOR]

This paper deals with the synchronization control of a class of delayed neural networks using a fast fixed-time control theory. By employing Lyapunov stability theory, a novel sufficient criterion is derived such that two neural networks can be synchronized within a fixed-time. Compared with some existing results, the proposed controller can render two neural networks faster synchronized. A numerical example is given to demonstrate the effectiveness of the criterion. [ABSTRACT FROM AUTHOR]

This paper is concerned with mean square exponential synchronization for two classes of Markovian switching complex networks (MSCNs) under linear negative control scheme from synchronization control cost viewpoint. Two classes of MSCNs are considered. In order to analyze synchronization controllability for the two classes of MSCNs from synchronization control cost viewpoint, synchronization control cost and synchronization controllability are defined, respectively. By utilizing M-matrix properties, a novel Lyapunov function and the stochastic analysis techniques, sufficient criteria of mean square synchronization and global synchronization for the two classes of MSCNs under feedback control are derived. Three numerical examples and simulations are given to illustrate the following conclusions: (1) the two classes of MSCNs under the same linear negative feedback controller can achieve mean square exponential synchronization and global synchronization if they satisfy sufficient conditions of mean square exponential synchronization; (2) by computing synchronization control cost, we obtain that global synchronization controllability for the first class of MSCNs may perhaps stronger or poorer than that of the second class of MSCNs with time-varying delays. [ABSTRACT FROM AUTHOR]