A Contribution to the Polynomial Eigen Problem

The relationship between eigenstructure (eigenvalues
and eigenvectors) and latent structure (latent roots and latent vectors)
is established. In control theory eigenstructure is associated with
the state space description of a dynamic multi-variable system and
a latent structure is associated with its matrix fraction description.
Beginning with block controller and block observer state space forms
and moving on to any general state space form, we develop the
identities that relate eigenvectors and latent vectors in either direction.
Numerical examples illustrate this result. A brief discussion of the
potential of these identities in linear control system design follows.
Additionally, we present a consequent result: a quick and easy
method to solve the polynomial eigenvalue problem for regular matrix
polynomials.

• Malika Yaici
• Kamel Hariche
• Tim Clarke

• Eigenvalues/Eigenvectors
• Latent values/vectors
• Matrix fraction description
• State space description.

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