p-moment stability of stochastic impulsive differential equations and its application in impulsive control

Abstract

The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impulsive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.p-moment stability, impulsive, white-noise, stochastic differential equations

Stability of impulsive stochastic functional differential systems in terms of two measures via comparison approach

“…Hence, (12) holds. Combining (12), (13) and condition (ii), we have Eh(t, x(t)) < ε, t t 0 + T proving the (h 0 , h)-asymptotical stability of system (1).…”

“…In recent years, stochastic effect to the stability of impulsive differential systems (IDSs) and IFDSs has attracted great interest of many researchers. Consequently, several interesting results on impulsive stochastic differential systems (ISDSs) and impulsive stochastic functional differential systems (ISFDSs), including impulsive stochastic delay differential systems (ISDDSs), have been reported [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…In particular, by employing Lyapunov-like function method and comparison principle, [10] obtained some sufficient conditions ensuring the existence, uniqueness and stability of solutions for ISDSs, and [11] investigated the stability in terms of two measures of ISDSs. Moreover, [12] and [13] applied comparison principle in chaos control. In [14], fixed point approach was successfully applied to investigate the asymptotic stability in pth moment of mild solutions of ISDSs.…”

p-th moment exponential stability of stochastic differential equations with impulse effect

“…Note that the conditions of Theorem 3 in [15] when dealing with (1) is stronger than the conditions of Theorem 1. And especially when I k (x) = 0, Theorem 1 in [16] and Theorem 8 in [18] can be obtained directly from Theorem 1.…”

Performance of a New Geometry of Deoiling Hydrocyclones: Experiments and Numerical Simulations

“…Thus, in recent years, environmental agencies have increased their care for the disposal of produced water into the sea, rivers, and on land, estab-lishing more rigorous criteria pertaining to the oil content as well as the presence of heavy metals and certain chemicals. For such reasons, as well as the need to reuse the produced water, researchers have been looking for practical and highly efficient separation methods that provide an economical solution in order to reach environmental standards [10][11][12][13].…”