In this note, we provide a unified framework for the mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric known as an optimal transport, that assesses the distance between probability density functions enables the stability analysis. Without any assumption on the underlying jump process, this Wasserstein distance guarantees the mean square stabil...

This paper performs a joint analysis of control and coding for stability and performance of LTI systems connected over communication networks. We study the communication rate required for stability of the differential entropy and mean-square stability of the state estimation error. We show that the optimal control and coding problems in the minimization of an LQR cost are separable; we further ...

In this paper, we provide a new framework for mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric which defines an optimal transport cost between probability density functions enables the stability analysis. Without any assumptions on the nature of the underlying jump process, the convergence of the Wasserstein distance guarantees the mean squar...

The motion of a charged particle in a randomly varying uniform magnetic field is investigated. Stability of the mean position and mean square displacement are determined rigorously in the case of random binary variations (telegraph signal). It is found that the mean position can be stable if the fluctuating part of the magnetic field is large enough compared to the uniform background. The stabi...

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of ...

The problems of mean-square exponential stability and robust H∞ control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities LMIs . Then, H∞ performance is studied and robust H...

Abstract: In this paper, the mean square exponential stability of the periodic solution for stochastic reactiondiffusion high-order Cohen-Grossberg-Type BAM neural networks with time delays is investigated. By constructing suitable Lyapunov function, applying Itô formula and Poincaré mapping, we give some sufficient conditions to guarantee the mean square exponential stability of the periodic s...

A simple, yet powerful, learning method is presented by combining the famed kernel trick and the least-mean-square (LMS) algorithm, called the KLMS. General properties of the KLMS algorithm are demonstrated regarding its well-posedness in very high dimensional spaces using Tikhonov regularization theory. An experiment is studied to support our conclusion that the KLMS algorithm can be readily u...