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This article establishes a “robustness” type result, namely, delay tolerance for stable stochastic systems under suitable conditions. We study the delay tolerance for stable stochastic systems and delayed feedback controls of such systems, where the delay can be state-dependent or induced by the sampling-data. First, we consider systems with global Lipschitz continuous coefficients and show that when the original stochastic system without delay is pth moment exponentially stable, the system with small delays is still pth moment exponentially stable. In particular, when the pth moment exponential stability is based on Lyapunov conditions, we can obtain explicit delay bounds for moment exponential stability. Then, we consider a class of stochastic systems with nonglobal Lipschitz conditions and find a delay bound for almost sure and mean square exponential stability. As extension of the stability tolerance criteria, consensus, and tracking control of multiagent systems with measurement noises and nonuniform delays are studied. [ABSTRACT FROM AUTHOR]

This paper develops stochastic consentability of linear multiagent systems with time delays and multiplicative noises. First, the stochastic stability for stochastic differential delay equations driven by multiplicative noises is examined, and the existence of the positive definite solution for a class of generalized algebraic Riccati equations (GAREs) is established. Then, sufficient conditions are deduced for the mean square and almost sure consentability and stabilization based on the developed stochastic stability and GAREs. Consensus protocols are designed for linear multiagent systems with undirected and leader-following topologies. It is revealed that multiagent consentability depends on certain characterizing system parameters, including linear system dynamics, communication graph, channel uncertainties, and time delay of the deterministic term. It is shown that a second-order integrator multiagent system is unconditionally mean square and almost surely consentable for any given noise intensities and time delay, and that the mean square and almost sure consensus can be achieved by carefully choosing the control gain according to certain explicit conditions. [ABSTRACT FROM PUBLISHER]