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This paper is concerned with the \mathcal H\infty filtering problem for a class of time-varying nonlinear delayed system under high-rate communication network and stochastic protocol (SP). The communication between the sensors and the state estimator is implemented via a shared high-rate communication network in which multiple transmissions are generated between two adjacent sampling instants of sensors. At each transmission instant, only one sensor is allowed to get access to the communication network in order to avoid data collisions and the SP is employed to determine which sensor obtains access to the network at a certain instant. The mapping technology is applied to characterize the randomly switching behavior of the data transmission resulting from the utilization of the SP. The aim of the problem addressed is to design an estimator such that the \mathcal H\infty disturbance attenuation level is guaranteed for the estimation error dynamics over a given finite horizon. Sufficient conditions are derived for the existence of the finite-horizon filter satisfying the prescribed \mathcal H\infty performance requirement, and the explicit expression of the time-varying filter gains is characterized by resorting to a set of recursive matrix inequalities. Simulation results demonstrate the effectiveness of the proposed filter design scheme. [ABSTRACT FROM AUTHOR]

Abstract-Stochastic approximation methods have been extensively studied in the literature for solving systems of stochastic equations and stochastic optimization problems where function values and first order derivatives are not observable but can be approximated through simulation. In this paper, we investigate stochastic approximation methods for solving stochastic variational inequality problems (SVIP) where the underlying functions are the expected value of stochastic functions. Two types of methods are proposed: stochastic approximation methods based on projections and stochastic approximation methods based on reformulations of SVIP. Global convergence results of the proposed methods are obtained under appropriate conditions. [ABSTRACT FROM AUTHOR]

In this paper, the concept of self-bounded controlled invariance is extended to nonstrictly proper systems. Moreover, its use in connection with the disturbance decoupling problem with internal stability is investigated in the case where the feedthrough matrices from the control input and from the disturbance to the output to be decoupled are possibly nonzero. [ABSTRACT FROM AUTHOR]