This paper investigates the robust stabilization problem for a class of neutral uncertain stochastic systems with Markovian switching and time-varying delays. The objective is to design a feedback controller based on discrete-time state observations and continuously available mode information such that the closed-loop system achieves robust exponential stability in the mean-square sense against all admissible uncertainties. By employing the Razumikhin technique, we derive sufficient conditions for mean-square exponential stability of the controlled system without imposing any differentiability assumption on the time-varying delay—only boundedness is required. This significantly relaxes the commonly used conditions in the existing literature, where the delay is required to be differentiable with a derivative bounded by a constant strictly less than one, or to satisfy a measure-type condition for non-differentiable delays. On this basis, the desired discrete-time feedback controller is explicitly constructed via linear matrix inequalities (LMIs), and an explicit estimate of the corresponding Lyapunov exponent is provided, which is rarely addressed in existing discrete-time feedback control results for neutral systems. Finally, numerical examples illustrate the effectiveness of the controller and demonstrate the applicability of the proposed criterion to a sampling-holding delay that violates commonly used differentiability and measure-type delay conditions.

This paper investigates how opinion dynamics with memory effects and random communication uncertainties achieve consensus in an inhomogeneous Hegselmann–Krause (H-K) model. The Caputo fractional derivative is introduced to describe the influence of historical opinions, while multiplicative noise captures random disturbances in communication. We establish sufficient conditions under which all followers almost surely converge to the leader’s opinion. Moreover, we characterize the algebraic (power-law) convergence behavior determined by the fractional order. The analysis is based on fractional Lyapunov techniques and fractional Grönwall estimates, which enable the treatment of the nonlinear stochastic system with leadership. The results reveal how memory effects, leadership strength and stochastic perturbations jointly influence consensus formation. Numerical simulations are provided to verify the theoretical results and illustrate the effects of the model parameters on the convergence dynamics.