Eigenvalue assignment in linear optimal-control systems via reduced-order models

Abstract
Algorithms are currently available for the solution of certain types of optimal-eigenvalue-assignment problems in which the eigenvalues of a given system are required to be shifted into preassigned locations or region while also minimising an appropriate quadratic-performance criterion. All the known methods for a solution of the above problem are based on manipulation of the original nth-order system matrices even if only r eigenvalues (r ≥ n) of the original system are to be reassigned. On the contrary, the method proposed in this paper, for a solution of the above problem, employs an rth-order equivalent model, which leads to a solution via manipulation of rth-order matrices only. The method also ensures that the remaining n — r eigenvalues of the original system are not disturbed and are carried over to the resultant feedback system. It has been shown in the paper that the suggested procedure brings about a considerable saving in computation time, and also requires less computer storage. Two numerical examples have been included to illustrate the suggested technique.

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