TY - JOUR
T1 - Stability of solutions for stochastic impulsive systems via comparison approach
AU - Liu, Bin
PY - 2008
Y1 - 2008
N2 - This note studies stability problem of solutions for stochastic impulsive systems. By employing Lyapunov-like function method and Itô's formula, comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established. Based on these comparison principles, the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system. As the application, the stability results are used to design impulsive control for the stabilization of unstable stochastic systems. Finally, one example is given to illustrate the obtained results.
AB - This note studies stability problem of solutions for stochastic impulsive systems. By employing Lyapunov-like function method and Itô's formula, comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established. Based on these comparison principles, the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system. As the application, the stability results are used to design impulsive control for the stabilization of unstable stochastic systems. Finally, one example is given to illustrate the obtained results.
KW - Comparison principle
KW - Impulsive control
KW - Itô's formula
KW - Stability
KW - Stochastic impulsive system (SIS)
UR - http://www.scopus.com/inward/record.url?scp=54349094098&partnerID=8YFLogxK
U2 - 10.1109/TAC.2008.930185
DO - 10.1109/TAC.2008.930185
M3 - Article
SN - 0018-9286
VL - 53
SP - 2128
EP - 2133
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 9
ER -