Right coprime factorisations using system upper Hessenberg forms—the multi-input system case

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Right coprime factorisations using system upper Hessenberg forms—the multi-input system case

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Based on a method for right coprime factorisations of linear systems using matrix elementary transformations, it is shown that a very simple iteration formula exists for right coprime factorisations of multi-input linear systems in system upper Hessenberg forms. This formula gives directly the coefficient matrices of the pair of solutions to the right coprime factorisation of the system Hessenberg form, and involves only inverses of a few triangular matrices and some matrix products and summations. Based on this formula, a simple, efficient procedure for determining a right coprime factorisation of a multi-input linear system is proposed, which first converts a given linear system into its system Hessenberg form using some orthogonal similarity transformations and then applies the iteration formula to the converted system Hessenberg form. An example demonstrates the use of the approach.

Inspec keywords: linear systems; controllability; matrix algebra; iterative methods

Other keywords: iterative method; Hessenberg forms; triangular matrix; coprime factorisations; linear systems

Subjects: Algebra; Interpolation and function approximation (numerical analysis); Control system analysis and synthesis methods

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