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access icon free Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations

  • Author(s): Ying Zhang 1 ; Ai-Guo Wu 1 ; Chun-Tao Shao 2
    • View affiliations
    • Affiliations: 1: Shenzhen Graduate School, Harbin Institute of Technology, Nanshan District, Shenzhen, 518055, People's Republic of China ;
      2: Department of Control Science and Engineering, Harbin Institute of Technology at Weihai, Weihai, 264209, People's Republic of China
  • Source: Volume 11, Issue 10, 23 June 2017, p. 1554 – 1560
    DOI:  10.1049/iet-cta.2016.1601 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 20/12/2016, Accepted 11/03/2017, Revised 09/02/2017, Published 16/03/2017
Errata or comment

An implicit iterative algorithm is established for solving a class of Lyapunov matrix equations appearing in the discrete-time stochastic systems with multiplicative noise. This algorithm contains a tuning parameter which can be appropriately chosen such that it has better convergence performance. Some convergence conditions have been derived for the proposed iterative algorithm, and for a special case an approach is given to choose the optimal tuning parameter such that the algorithm has the best convergence performance. In addition, the properties of boundedness and monotonicity of the proposed algorithm are also investigated when the corresponding stochastic system is asymptotically mean-square stable.

Inspec keywords: iterative methods; stochastic systems; mean square error methods; convergence of numerical methods; discrete time systems; Lyapunov matrix equations; asymptotic stability

Other keywords: convergence performance; implicit iterative algorithm; multiplicative noise; asymptotically mean-square stable stochastic system; optimal tuning parameter; discrete-time stochastic Lyapunov matrix equations; monotonicity properties; boundedness properties

Subjects: Discrete control systems; Linear algebra (numerical analysis); Time-varying control systems; Stability in control theory; Interpolation and function approximation (numerical analysis)

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Errata: ‘Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations’
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