New algorithm for the optimal stabilisation of linear systems using pole-assignment techniques

In this paper, a new algorithm for the design of optimal controllers of large-scale linear systems using a pole-assignment technique to achieve a desired degree of stability is presented. The method is based on obtaining the weighting matrix Q of a suitable quadratic performance index and the optimal-control matrix F that correspond to the desired closed-loop eigenvalues of the system. To achieve this, a reduced model, retaining only those eigenvalues of the original system which are to be shifted, is considered, and it has been proved that, if a suitable weighting matrix Q¿ and an optimal control matrix F¿ of the reduced model having the desired set of eigenvalues are found, a simple matrix manipulation yields the weighting matrix Q and the control matrix F of the original large-scale system. The algorithm has been illustrated with an example.