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International Journal of Stochastic Analysis
Volume 2013 (2013), Article ID 281473, 5 pages
Research Article

The LMI Approach for Stabilizing of Linear Stochastic Systems

Faculty of Economics and Business Administration, Sofia University “St. Kliment Ohridski,”, 125 Tsarigradsko Shosse Boulevard, bl.3, 1113 Sofia, Bulgaria

Received 28 April 2013; Accepted 26 July 2013

Academic Editor: Josefa Linares-Pérez

Copyright © 2013 Ivan Ivanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Stochastic linear systems subjected both to Markov jumps and to multiplicative white noise are considered. In order to stabilize such type of stochastic systems, the so-called set of generalized discrete-time algebraic Riccati equations has to be solved. The LMI approach for computing the stabilizing symmetric solution (which is in fact the equilibrium point) of this system is studied. We construct a new modification of the standard LMI approach, and we show how to apply the new modification. Computer realizations of all modifications are compared. Numerical experiments are given where the LMI modifications are numerically compared. Based on the experiments the main conclusion is that the new LMI modification is faster than the standard LMI approach.