×

Robust control design through the attractive ellipsoid technique for a class of linear stochastic models with multiplicative and additive noises. (English) Zbl 1273.93167

Summary: This paper concerns the robust ‘practical’ stabilization for a class of linear controlled stochastic differential equations subject to both multiplicative and additive stochastic noises. Sufficient conditions of the stabilization are provided in two senses. In the first sense, it is proven that almost all trajectories of the stochastic model converge in a ‘mean-square sense’ to a bounded zone located in an ellipsoidal set, while the second one ensures the convergence to a zero zone in probability one. The considered control law is a linear state feedback. The stabilization problem is converted into the corresponding attractive averaged ellipsoid ‘minimization’ under some constraints of Bilinear Matrix Inequalities (BMIs) type. Some variables permit to represent the BMIs problem in terms of Linear Matrix Inequalities (LMIs) problem, which are resolved in a straight manner, using the conventional LMI-MATLAB toolbox. Finally, the numerical solutions of a benchmark example and a practical example are presented to show the efficiency of the proposed methodology.

MSC:

93E12 Identification in stochastic control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93B35 Sensitivity (robustness)
93D21 Adaptive or robust stabilization

Software:

LMI toolbox; Matlab
PDFBibTeX XMLCite
Full Text: DOI Link