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This research focuses on the stochastic functional differential equations driven by G-Brownian motion (G-SFDEs) with infinite delay. It is proved that the trivial solution of a G-SFDE with infinite delay is exponentially stable in mean square. An example is also presented to illustrate the effectiveness of the obtained theory.

This study is concerned with the stabilization analysis and controller design for networked systems with stochastic sampling and two‐channel deception attacks. First, we give a general matrix decomposition approach which is applicable to scenarios where the system matrix A$A$ contains complex‐value eigenvalues. Then, a discrete stochastic framework is established for a class of networked systems which considers the joint effects of sampling errors and two‐channel deception attacks. Utilizing the matrix decomposition approach introduced in this study, it becomes feasible to decouple the expectation operations for specific coupling matrices characterized by substantial nonlinearity and randomness. Based on this, a stabilization controller is constructed that ensures the exponential mean‐square stability of the resulting discrete stochastic system. Finally, three simulation examples are provided to validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the H∞$$ {H}_{\infty } $$ saturated control problems of networked systems with random sampling periods and stochastic transmission delays are investigated. The main issue is to design an H∞$$ {H}_{\infty } $$ saturated controller such that the controlled close‐loop system is exponentially mean‐square stable with a desired H∞$$ {H}_{\infty } $$ performance. A matrix exponential which is different from some existing literature is used to reconstruct the discrete‐time stochastic system to an equivalent yet tractable augmented model without any additional conditional constraint. In virtue of reduced‐order confluent Vandermonde matrix approach and Kronecker product operation, the stability condition in terms of linear matrix inequality is derived and then the desired H∞$$ {H}_{\infty } $$ saturated controller is designed. It should be emphasized that the improved method can also be used for the stability analysis and controller design when the system matrix contains complex roots. Finally, two numerical examples and a three‐axis milling machine system are utilized to manifest the reliability and practicality of the designed strategy. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this brief note, a probability theory approach is proposed to investigate the stability analysis issue for a class of networked sampled-data systems with packet dropouts. The continuous-time linear system under consideration is first transformed into a discrete-time system, where the system matrix of the discrete-time system is characterized by stochastic characteristic. Then, by the matrix exponential computation, an equivalent discrete-time stochastic system is established. Based on this, a controller is designed by the law of total expectation, which guarantees the stochastic stability of the closed-loop stochastic system. Finally, a numerical example and an example using power grid with IEEE 4-bus line are used to verify the effectiveness and applicability of the proposed design algorithm. [ABSTRACT FROM AUTHOR]

This article is concerned with the stabilization problem for a class of networked systems subject to successive packet losses. Different from the input delay approach used in some existing literature, the continuous‐time system under consideration is first converted into a discrete‐time stochastic system with system matrices subject to stochastic characteristic. In order to deal with the difficulties in the calculations of mathematical expectations of both matrix exponential and integral of matrix exponential function, the upper bound of successive packet losses and packet drop rate are assumed to be known and then the probabilities of the number of successive packet losses taking each value in a bounded set are calculated. Based on this, stability criteria are derived by recurring to the law of total expectation, which guarantee the exponential mean‐square stability of resulting closed‐loop discrete‐time stochastic system with a prescribed H∞ performance. Moreover, a controller design procedure is then proposed. Finally, to verify the analysis results and testify the effectiveness and applicability of the designed algorithm, a numerical simulation example is given. [ABSTRACT FROM AUTHOR]

This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method. [ABSTRACT FROM AUTHOR]

In this article, the stochastic analysis and H ∞ controller design problems of networked systems with packet dropouts and false data injection attacks are investigated. Different from the existing literature, we focus on the linear networked systems with external disturbances and both sensor-controller channel and controller-actuator channel are studied. First, we present a discrete-time modeling framework that leads to a stochastic closed-loop system with randomly varying parameters. To facilitate the analysis and H ∞ control of resulting discrete-time stochastic closed-loop system, an equivalent yet analyzable stochastic augmented model is further constructed by matrix exponential computation. Based on this model, a stability condition is derived in the form of linear matrix inequality (LMI) with the aid of a reduced-order confluent Vandermonde matrix, Kronecker product operation, and law of total expectation. Specifically, the dimension of the LMI obtained in this article does not increase as the upper bound of consecutive packet dropouts does, which is also different from the existing literature. Subsequently, a desired H ∞ controller is obtained such that the original discrete-time stochastic closed-loop system is exponentially mean-square stable with a prescribed H ∞ performance. Finally, a numerical example and a direct current motor system are exploited to substantiate the effectiveness and practicability of the designed strategy.

This article addresses the issue of output-feedback consensus control of multiagent systems under the directed topology and subject to bounded external disturbances. By employing a smooth time-varying function, a distributed practical predefined-time (PPT) observer is developed to estimate the reference trajectory for the entire team (i.e., the leader's state) and a practical preset-time extended-state observer is also proposed to estimate bounded disturbances and unmeasurable system states. Next, a novel continuous and nonsingular PPT consensus control law is designed on the basis of the observers. Furthermore, the designed control protocol can achieve PPT stability, that is, consensus tracking errors are enforced to a neighborhood around zero within a predetermined time, which can be specified a priori, independent of initial states of agents and/or any other design parameters. Finally, illustrative numerical examples, including a comparative one, are provided to demonstrate the performance of the present predefined-time control approach.

This article focuses on the sampled-data synchronization issue for a class of complex dynamical networks (CDNs) subject to noisy sampling intervals and successive packet losses. The sampling intervals are subject to noisy perturbations, and categorical distribution is used to characterize the sampling errors of noisy sampling intervals. By means of the input delay approach, the CDN under consideration is first converted into a delay system with delayed input subject to dual randomness and probability distribution characteristic. To verify the probability distribution characteristic of the delayed input, a novel characterization method is proposed, which is not the same as that of some existing literature. Based on this, a unified framework is then established. By recurring to the techniques of stochastic analysis, a probability-distribution-dependent controller is designed to guarantee the mean-square exponential synchronization of the error dynamical network. Subsequently, a special model is considered where only the lower and upper bounds of delayed input are utilized. Finally, to verify the analysis results and testify the effectiveness and superiority of the designed synchronization algorithm, a numerical example and an example using Chua's circuit are given.