An efficient iterative method for matrix sign function with application in stability analysis of control systems using spectrum splitting

The goal of this study is to construct a novel iterative method to compute the matrix sign function using a different approach. It is discussed that the new method is globally convergent and asymptotically stable. It achieves the sixth order of convergence and only requires five matrix–matrix multip...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-08, Vol.47 (12), p.9450-9468
Main Authors: Sharma, Pallvi, Kansal, Munish
Format: Article
Language:English
Subjects:
Control stability
Control systems
Control theory
Dynamical systems
eigenvalue separation
Eigenvalues
global convergence
iterative method
Iterative methods
Matrices (mathematics)
matrix iteration
matrix sign function
Stability analysis
Systems analysis
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Summary:The goal of this study is to construct a novel iterative method to compute the matrix sign function using a different approach. It is discussed that the new method is globally convergent and asymptotically stable. It achieves the sixth order of convergence and only requires five matrix–matrix multiplications. The obtained results are extended to compute the number of eigenvalues of a matrix in a specified region of the complex plane. This is done by performing appropriate sequence of matrix sign computations. An application of this technique has been discussed in stability analysis of linear time‐invariant dynamic systems in control theory. Numerical results have been given to justify the effectual performance and superiority of the proposed method. Matrices of various sizes have been considered for this purpose.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10077