access icon free Explicit iterative algorithms for solving coupled discrete-time Lyapunov matrix equations

© The Institution of Engineering and Technology
Received 26/04/2016, Accepted 27/08/2016, Revised 25/08/2016, Published 01/09/2016

In this study, the authors aim to study explicit iterative algorithms for solving coupled discrete-time Lyapunov matrix equations. First, an explicit iterative algorithm based on fixed point theory of dynamic equations is presented via adding a tuning parameter. Second, a necessary and sufficient condition is provided for the convergence of the proposed algorithm. Moreover, the optimal value of the tuning parameter is derived for the fastest convergence of the algorithm. Third, by using the latest updated information, a modified version of the presented explicit iterative algorithm is also established with a necessary and sufficient condition being provided to guarantee the convergence of the modified algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed algorithms.

Inspec keywords: convergence; discrete time systems; iterative methods; Lyapunov matrix equations

Other keywords: dynamic equations; fixed point theory; explicit iterative algorithms; tuning parameter; coupled discrete-time Lyapunov matrix equations; convergence

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

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