TY - GEN
T1 - Robust stabilization of linear stochastic differential models with additive and multiplicative diffusion via attractive ellipsoid techniques
AU - Lozada-Castillo, Norma B.
AU - Alazki, Hussain
AU - Poznyak, Alexander S.
PY - 2011
Y1 - 2011
N2 - Linear controlled stochastic differential equations (LCSDE) subject to both multiplicative and additive stochastic noises are considered. We study a robust "practical" stabilization for this class of LCSDE meaning that almost all trajectories of this stochastic model converges in a "mean-square sense" to a bounded zone located in an ellipsoidal set. Also, we present a result related to convergence in probability one sense to a zero zone. The considered stabilizing feedback is supposed to be linear. This problem is shown to be converted into the corresponding attractive averaged ellipsoid "minimization" under some constraints of BMI's (Bilinear Matrix Inequalities) type. The application of an adequate coordinate changing transforms these BMI's into a set of LMI's (Linear Matrix Inequalities) that permits to use directly the standard MATLAB - toolbox. A numerical example is used to illustrate the effectiveness of this methodology.
AB - Linear controlled stochastic differential equations (LCSDE) subject to both multiplicative and additive stochastic noises are considered. We study a robust "practical" stabilization for this class of LCSDE meaning that almost all trajectories of this stochastic model converges in a "mean-square sense" to a bounded zone located in an ellipsoidal set. Also, we present a result related to convergence in probability one sense to a zero zone. The considered stabilizing feedback is supposed to be linear. This problem is shown to be converted into the corresponding attractive averaged ellipsoid "minimization" under some constraints of BMI's (Bilinear Matrix Inequalities) type. The application of an adequate coordinate changing transforms these BMI's into a set of LMI's (Linear Matrix Inequalities) that permits to use directly the standard MATLAB - toolbox. A numerical example is used to illustrate the effectiveness of this methodology.
KW - Attractive Ellipsoid Method
KW - Linear Matrix Inequalities
KW - Stochastic differential equations
UR - http://www.scopus.com/inward/record.url?scp=84855791975&partnerID=8YFLogxK
U2 - 10.1109/ICEEE.2011.6106685
DO - 10.1109/ICEEE.2011.6106685
M3 - Contribución a la conferencia
AN - SCOPUS:84855791975
SN - 9781457710117
T3 - CCE 2011 - 2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control, Program and Abstract Book
BT - CCE 2011 - 2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control, Program and Abstract Book
T2 - 2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2011
Y2 - 26 October 2011 through 28 October 2011
ER -