Impulsive stabilization of stochastic functional differential equations

AbstractThis paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov–Razumikhin method. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An example with its numerical simulation is presented to illustrate the main results

Impulsive stabilization of high-order nonlinear retarded differential equations

summary:In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods

Adaptive sliding mode observers in uncertain chaotic cryptosystems with a relaxed matching condition

We study the performance of adaptive sliding mode observers in chaotic synchronization and communication in the presence of uncertainties. The proposed robust adaptive observer-based synchronization is used for cryptography based on chaotic masking modulation (CM). Uncertainties are intentionally injected into the chaotic dynamical system to achieve higher security and we use robust sliding mode observer design methods for the uncertain nonlinear dynamics. In addition, a relaxed matching condition is introduced to realize the robust observer design. Finally, a Lorenz system is employed as an illustrative example to demonstrate the effectiveness and feasibility of the proposed cryptosyste