In this work, a new class of stochastic gradient algorithm is developed based on q-calculus. Unlike the existing q-LMS algorithm, the proposed approach fully utilizes the concept of q-calculus by incorporating time-varying q parameter. The proposed enhanced q-LMS (Eq-LMS) algorithm utilizes a novel, parameterless concept of error-correlation energy and normalization of signal to ensure high con...

This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almos...

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associati...

We investigate the instabilities of a linear damped oscillator due to fluctuations of the damping parameter. The fluctuations are driven either by Gaussian white noise or Poisson white noise (white shot noise). We consider three notions of stability. The first two are the well-known notions of stability in the mean and stability in the mean square. We introduce the concept of thermodynamic stab...

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy Cohen-Grossberg neural networks with mixed delays is considered. Based on M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and global exponential stability in mean square means of the equilibrium point for the addressed impulsive st...

This article is concerned with stability analysis of a linear discrete-time dynamic quantizer system with packet loss. First, several modifications are made to the original dynamic quantizer to make it easier to realize. Then communication channel subject to packet loss of Bernoulli distribution from the quantizer to the plant input is considered. Moreover, based on Lyapunov function approach, ...

This paper highlights, both analytically and by simulations, some interesting phenomena regarding the behavior of ensemble-average learning curves of adaptive filters that may have gone unnoticed. Among other results, the paper shows that even ensemble-average learning curves of single-tap LMS filters actually exhibit two distinct rates of convergence: one for the initial time instants and anot...