In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, definition is given, necessary sufficient conditions for derived. Secondly, several via a state feedback controller an output obtained. Furthermore, explicit expressions static Finally, two examples given to illustrate validity above results.

Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-step θ method is proposed to numerically solve the stochastic differential ...

*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solution...

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model p...

Abstract In this paper a model of Hopfield’s graded response neural network is investigated. A whose neurons are subject to certain impulsive state displacement at random times considered. The set up and studied. presence moments impulses in the leads change solutions stochastic processes. Also, we use Riemann–Liouville fractional derivative adequately long-term memory nonlocality networks. We ...

In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared with a non-cooperative agent which represents the average of the network. The analysis provides conditions under which diversity in the filter parameters is be...

Stability analysis of numerical methods for ordinary diierential equations is motivated by the question \for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?" We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the Theta Method. We extend some mean-squ...