Symmetry preserving partial pole assignment for the standard and generalized eigenvalue problems

Sylvan Elhay


Many real-life state feedback control systems are modelled by a set of
single-input, time-invariant linear equations. Often, these lead to a
pair of matrices which are real and symmetric. The pole assignment
problem requires us to find a state feedback control which gives
the closed loop matrices a prescribed set of poles. Commonly used
controls produce a closed loop matrix which is no longer symmetric.
In this paper we present an explicit solution for a new symmetry
preserving partial pole assignment method for the generalized
eigenvalue problem and for the standard eigenvalue problem. The
methods are demonstrated on illustrative examples and can produce
computationally accurate solutions for even quite large systems.

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.