The LMI Approach for Stabilizing of Linear Stochastic Systems

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 newmodification of the standard LMI approach, andwe showhow to apply the newmodification. Computer realizations of all modifications are compared. Numerical experiments are givenwhere the LMImodifications are numerically compared. Based on the experiments the main conclusion is that the new LMI modification is faster than the standard LMI approach.