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This work deals with the construction of finite difference solutions of random advection Cauchy type partial differential equation containing uncertainty through the coefficient of the velocity. Under appropriate hypothesis on the...
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This work deals with the construction of finite difference solutions of random advection Cauchy type partial differential equation containing uncertainty through the coefficient of the velocity. Under appropriate hypothesis on the velocity random variable, we establish that the constructed random finite difference solution is mean square consistent and mean square stable over the whole real line. In addition, the main statistical functions, such as the mean, of the approximate solution stochastic process generated by truncation of the exact finite difference solution are given. Finally, we apply the proposed technique to several illustrative examples which show our discussing for the mean square stability.
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Abstract This article investigates the mean‐square strong stability and stabilization of a discrete‐time stochastic system corrupted by multiplicative noises. First, the definition of the mean‐square (MS) strong stability is ad...
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Abstract This article investigates the mean‐square strong stability and stabilization of a discrete‐time stochastic system corrupted by multiplicative noises. First, the definition of the mean‐square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS‐strong stability are derived. Moreover, the relationship between MS‐strong stability and MS‐stability is given. Second, some necessary and sufficient conditions of the MS‐strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.
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This paper investigates the issue of output feedback stabilization for networked control systems. The randomly sampled measurement process caused by the time-varying channel load is modeled as a Markov chain. An event-driven trans...
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This paper investigates the issue of output feedback stabilization for networked control systems. The randomly sampled measurement process caused by the time-varying channel load is modeled as a Markov chain. An event-driven transmitter, which depends on the measurement sampling period, is introduced to transmit the control signal. In order to achieve a less conservative result, a novel output feedback controller, including both sampling and event-driven transmitter-induced delay indexes, is proposed. The sufficient and necessary condition for the mean-square stability, the stochastic stability, and the exponential mean-square stability for the closed-loop system is established, and the controller is designed by using the cone complementarity linearization approach. Finally, based on the ZigBee real communication channel, a cart and inverted pendulum system is shown to demonstrate the effectiveness of the proposed method.
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In this article, we are concerned with the consensus problem of multiagent system where the channels from each agent's control input to the plant are fading nonidentically. Two problems have been extensively studied. One is the co...
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In this article, we are concerned with the consensus problem of multiagent system where the channels from each agent's control input to the plant are fading nonidentically. Two problems have been extensively studied. One is the consentable problem when the current state information is available for the controller. The other is that the state information is delayed for the controller in which we propose a novel predictorlike control protocol. It is obtained that the multiagent system with system matrices A = B = 1 is mean-square consentable for both problems. In particular, the mean-square consensus value is the average of all agents' initial states. Furthermore, for the multiagent system with general dynamics, sufficient conditions have been obtained in terms of two parameterized Riccati inequality/equation for both problems, respectively.
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This paper investigates the stability of linear stochastic delay differential equations with infinite Markovian switchings. Some novel exponential stability criteria are first established based on the generalized It ?
This paper investigates the stability of linear stochastic delay differential equations with infinite Markovian switchings. Some novel exponential stability criteria are first established based on the generalized It ? formula and linear matrix inequalities. Then, a new sufficient condition is proposed for the equivalence of 4 stability definitions, namely, asymptotic mean square stability, stochastic stability, exponential mean square stability with conditioning, and exponential mean square stability. In particular, our results generalize and improve some of the previous results. Finally, two examples are given to illustrate the effectiveness of the proposed results.
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By using successive approximation, we prove the existence and uniqueness result for a class of neutral functional stochastic differential equations driven both by the cylindrical Brownian motion and by the Poisson point processes ...
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By using successive approximation, we prove the existence and uniqueness result for a class of neutral functional stochastic differential equations driven both by the cylindrical Brownian motion and by the Poisson point processes in a Hilbert space with non-Lipschitzian coefficients.
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Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a...
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Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis in the paper confirms that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own. When this occurs, cooperation over the network leads to a catastrophic failure of the estimation task. This phenomenon does not occur for diffusion networks: we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology. Simulation results support the theoretical findings.
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We present a unified framework to analyze the mean and mean-square stability of a large class of adaptive filters. We do this without obtaining a full transient model, allowing us to acquire sufficient conditions on the stability ...
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We present a unified framework to analyze the mean and mean-square stability of a large class of adaptive filters. We do this without obtaining a full transient model, allowing us to acquire sufficient conditions on the stability without assuming a given statistical distribution for the input regressors. We also apply the proposed framework to some popular adaptive filtering schemes, showing that in some cases the sufficient conditions derived are very tight and even necessary too.
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The existence of a strong solution of the linear stochastic partial differential equation (LSPDE) in the corresponding space with random parameters is proved. The sufficient conditions are obtained for the asymptotic stability and...
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The existence of a strong solution of the linear stochastic partial differential equation (LSPDE) in the corresponding space with random parameters is proved. The sufficient conditions are obtained for the asymptotic stability and mean square instability of the strong solution of the LSPDE.
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The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analy...
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The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical insights into the performance of this algorithm, we examine its mean-square performance and derive theoretical expressions for its transient and steady-state mean-square deviation. Our methodology is inspired by the principle of energy conservation in adaptive filters. Simulation results corroborate the accuracy of the derived formula.
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