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The LMI Approach for Stabilizing of Linear Stochastic Systems

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  • Ivan Ivanov

Abstract

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.

Suggested Citation

  • Ivan Ivanov, 2013. "The LMI Approach for Stabilizing of Linear Stochastic Systems," International Journal of Stochastic Analysis, Hindawi, vol. 2013, pages 1-5, August.
    • Handle: RePEc:hin:jnijsa:281473
    DOI: 10.1155/2013/281473
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    Cited by:

    1. Na Li & Yuan Wang & Zhen Wu, 2018. "An Indefinite Stochastic Linear Quadratic Optimal Control Problem with Delay and Related Forward–Backward Stochastic Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 722-744, November.

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