semi-Markov Switching Research Articles

A stochastic SIRS epidemic model with a saturation incidence under semi-Markovian switching

A stochastic SIRS epidemic model with a saturation incidence under semi-Markovian switching

Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies

In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.

Adaptive Output Formation Tracking for Nonlinear Multiagent Systems With Double Semi-Markovian Switching Topologies and Time-Varying Actuator Faults.

This article investigates adaptive output formation tracking control of nonlinear multiagent systems with time-varying actuator faults and unknown nonidentical control directions under double semi-Markovian switching topologies. Considering the dynamic changes of communication connections in uncertain environments, a double semi-Markov process is first introduced into the leader-follower structure to describe the random switching of communication topologies. Then, a novel adaptive distributed fault-tolerant output formation tracking control framework is established using the backstepping and Nussbaum gain technique to address matched/mismatched uncertainties and disturbances, time-varying actuator faults, and unknown nonidentical control directions. In this control framework, the independent variable of the Nussbaum function is designed as a non-negative function that monotonically increases with respect to time, thereby overcoming the presence of the absolute value of its derivative in the integration process. Based on the distributed structure, an adaptive fault-tolerant controller is further proposed to achieve the asymptotic output formation tracking in mean-square sense. The stability of the closed-loop nonlinear multiagent systems is analysed through the contradiction argument and Lyapunov theorem. The simulation example verifies the effectiveness of the proposed control strategy.

Reachable set control of singular semi-Markov jump multi-agent systems with input delay via state decomposition method

This paper addresses the challenge of reachable set estimation in singular multi-agent systems with time-delay and semi-Markov switching topologies. The primary goal is to construct an ellipsoid that encompasses all states originating from the origin. Furthermore, criteria for reachable sets with reduced conservatism are developed. The singular multi-agent systems are reduced by the Laplace matrix, then the Lyapunov–Krasovskii functional is constructed by using decomposed state vector. In addition, the sufficient conditions for the reachable set of singular multi-agent systems bounded by ellipsoids are given by matrix theory and linear matrix inequality. Numerical examples show that our results is effective.

Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control

A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.

Stability of a stochastic brucellosis model with semi-Markovian switching and diffusion.

To explore the influence of state changes on brucellosis, a stochastic brucellosis model with semi-Markovian switchings and diffusion is proposed in this paper. When there is no switching, we introduce a critical value and obtain the exponential stability in mean square when by using the stochastic Lyapunov function method. Sudden climate changes can drive changes in transmission rate of brucellosis, which can be modelled by a semi-Markov process. We study the influence of stationary distribution of semi-Markov process on extinction of brucellosis in switching environment including both stable states, during which brucellosis dies out, and unstable states, during which brucellosis persists. The results show that increasing the frequencies and average dwell times in stable states to certain extent can ensure the extinction of brucellosis. Finally, numerical simulations are given to illustrate the analytical results. We also suggest that herdsmen should reduce the densities of animal habitation to decrease the contact rate, increase slaughter rate of animals and apply disinfection measures to kill brucella.

Smc for discrete delayed semi-Markov switching systems

Smc for discrete delayed semi-Markov switching systems

Ultimate boundedness and stability of highly nonlinear neutral stochastic delay differential equations with semi-Markovian switching signals

The ultimate boundedness and stability of highly nonlinear neutral stochastic delay differential equations (NSDDEs) are investigated in this paper. Different from many previous works, the highly nonlinear NSDDEs with semi-Markov switching signals are considered for the first time in this paper. Meanwhile, the time delay function in this paper is only required to meet much more relaxed restrictions, which can invalidate plentiful methods with requirements on its derivatives for the stability of NSDDEs. To overcome this difficulty, several novel techniques to tackle NSDDEs with such a delay are developed. Furthermore, a crucial property on the ergodic semi-Markov process is established, which plays a key role in the proof on the existence and boundedness of global solution. The generalized Khasminskii-type theorems are established for the existence and uniqueness of global solution by applying new methods and this property, and the criteria for boundedness and stability are also provided. In particular, feasible measures are provided to deal with the neutral term in our stability criteria. Finally, the effectiveness is verified by a numerical example.

Novel Dynamic Event-Triggered Consensus Control of Multiagent Systems With Markovian Switching Topologies Under DoS Attacks.

This article focuses on the issue of novel dynamic event-triggered consensus control of multiagent systems (MASs) with denial-of-service (DoS) attacks. Different from the conventional Markovian switching topologies, the generally uncertain semi-Markovian (GUSM) switching topologies with partially unknown elements and time-dependent uncertainties are constructed for the leader-following MASs by considering the equipment performance and external uncertain environment influence. To save communication resources, the novel dynamic memory event-triggered strategy (DMETS) is presented to decrease the frequency of communication between agents. Some secure consensus control criteria are established for the MASs with GUSM switching topologies and DoS attacks due to the potential system communication disruption caused by attackers. Finally, two physical system examples are designed to prove the effectiveness of the presented method.

Adaptive protocol-based control for reaction-diffusion memristive neural networks with semi-Markov switching parameters

This study explores the asynchronous control of reaction-diffusion memristive neural networks (RDMNNs) using an innovative adaptive event-triggered protocol. The unique characteristic of RDMNNs is captured through a semi-Markov process model, wherein the probability density function of the duration time is contingent on two consecutive modes. A novel adaptive event-triggered strategy, specifically designed for the semi-Markov switching signal, is introduced to effectively reduce the network's bandwidth usage. The determination of thresholds in the adaptive triggering criterion is intricately associated with the system state residuals. Due to the mismatch between the controller and the RDMNNs, the protocol-based controller operates asynchronously. This asynchronous operation is characterized by a hidden semi-Markovian model. Utilizing stochastic Lyapunov functions that correlate with the detected and system modes, several sufficient criteria for designing an effective asynchronous controller are provided, thereby ensuring the stochastic stability of the system. Finally, the feasibility of the proposed scheme is validated through a simulated example.

Dynamic event-triggered synchronization for semi-Markovian switching inertial neural networks with generally uncertain transition rates in finite-time interval

This paper investigates the finite-time synchronization for inertial neural networks with stochastic switching parameters based on dynamic event-triggered protocol. Due to the complexity of network environment, semi-Markovian process is introduced into the modeling of inertial neural networks, in which the transition rates vary with the operating time. The dynamic event-triggered protocol is developed to determine whether the signal is transmitted, in which Zeno phenomenon is eliminated under limited bandwidth resources. The objective is to construct an appropriate dynamic event-triggered control law such that the drive-response system maintains finite-time synchronization under generally uncertain transition rates. Based on the Lyapunov functional theory, finite-time synchronization criterion is proposed for the related inertial neural networks. Furthermore, a dynamic event-triggered controller is constructed in a finite-time interval. A numerical example and an image encryption process are given to show the efficiency of the proposed method.

Group consensus of nonlinear semi-Markov multi-agent systems by a quantity limited controller

This paper solves the group consensus problem of incremental quadratic constraints nonlinear multi-agent systems with semi-Markov switching parameters via a quantity limited controller. The quantity limited controller is designed according to the stationary probability distribution of the system modes, and the number of controllers can be selected from 1 to the number of system modes. Therefore, the controller can be applied in cases where there is a mismatch between the number of system modes and the number of controllers. Next, the more general incremental quadratic constraint is used to handle the nonlinear terms. Finally, in the simulation section, the method of adding topology links is used to implement external equitable partitions of arbitrary topologies, and the validity of the proposed method is verified by a spring damping system.

Time-varying formation optimization tracking of multi-agent systems with semi-Markov switching topology

Time-varying formation optimization tracking of multi-agent systems with semi-Markov switching topology

Observer-based SMC for discrete semi-Markov switching models

This study focuses on the observer-based sliding mode control (SMC) for discrete stochastic switching models, where the semi-Markov kernel information is incomplete. Because the sensors do not always have direct access to the state vector in a complex environment, an observer-based output measurement is considered to estimate the system state. In contrast to previous works, the observer-based strategy is first investigated in studying the SMC for semi-Markov switching systems under the discrete framework. The sufficient condition for achieving mean-square stability is proposed to solve the desired observer and controller gains by utilizing the upper bound of sojourn time, along with the Lyapunov function that pertains to the system mode and the elapsed time. A mode-dependent SMC law is also constructed to ensure that the system state can reach the specified sliding region. Finally, the efficiency of the proposed method is demonstrated through the single-link robot arm model.

SMC for Discrete Semi-Markov Switching Slow Sampling Singularly Perturbed Models With Applications

SMC for Discrete Semi-Markov Switching Slow Sampling Singularly Perturbed Models With Applications

Event-triggered and stochastic-sampled consensus of nonlinear multi-agent systems under semi-Markov switching topology

This article investigates exponential mean square consensus (MSC) problem of leader–follower multi-agent systems (MASs). It is considered that the communication topology switches randomly and obeys a semi-Markov process. In view of possible data loss in information transmission, stochastic sampling scheme is introduced. Meanwhile, mode-dependent event-triggered control strategy based on sampled data is adopted to decrease communication broadband. The two cases that the transition rate matrix (TRM) of semi-Markov process is completely or partially known are respectively discussed. As a result, several sufficient conditions which can ensure to achieve exponential MSC are respectively deduced by means of stochastic Lyapunov theory and linear matrix inequality (LMI) theory. At last, two simulation tests corresponding to completely and partially known TRMs are designed to verify the correctness of the obtained conclusions.

A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies.

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.

Nonfragile state estimation for semi-Markovian switching CVNs with general uncertain transition rates: An event-triggered scheme

This paper tackles the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. The concerned transition rates of the semi-Markov process are uncertain, including both the completely unknown ones and the inaccurately known ones with known bounds. To reduce the communication burden, a particular event-triggered generator is constructed, which depends on the latest available measurement output and a predefined positive threshold. Combining the stochastic analysis method with the Lyapunov stability theory, some less conservative criteria are obtained to ascertain the global asymptotic stability of the estimation error system in the mean-square sense. In addition, by solving some matrix inequalities, the desired nonfragile estimator gains are explicitly designed. Finally, a numerical example with simulations is given to illustrate effectiveness of the established estimation scheme.

Stability of stochastic systems with semi-Markovian switching and impulses

The aim of this paper is to investigate the stochastic asymptotic stability of semi-Markov switched systems with mixed impulses. A novel definition of average impulse gain is given to estimate the intensity of the mixed impulses. Based on the multiple Lyapunov function approach and average impulse interval method, we provide sufficient conditions on the stochastic asymptotic stability for the semi-Markov switched system with impulses. Moreover, the influence of impulses on the system is estimated by applying the average impulse gain and average impulse interval method, which are not only suitable for synchronous impulses but also for asynchronous impulses. The theoretical results are demonstrated by two examples.

Finite-Time Annular Domain Stability and Stabilization of Stochastic Systems With Semi-Markovian Switching

In this paper, finite-time annular domain stability and stabilization of Itô stochastic systems with semi-Markovian switching are investigated, where the switching frequency is timevarying, and satisfies a unfixed polytope. A new inequality called reverse differential Gronwall inequality is proposed to address less conservative sufficient conditions for testing the finitetime annular domain stability, and its superiority to modified Gronwall inequality is analyzed. Moreover, sufficient conditions for the existence of state feedback and observer-based finitetime annular domain stabilizing controllers are obtained. In the sequel, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {L}$</tex-math></inline-formula> × <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -mode algorithm is presented for bridging the relationship between the adjustable parameters and the range of transition rates. Finally, an example is provided to illustrate the effectiveness of the proposed methods.