Pole placement by performance criterion modification

A procedure is presented that modifies the state weighting matrix Q and introduces a degree of relative stability into the original performance criterion to shape the resulting optimal dynamics by positioning the closed-loop eigenvalues along the real axis of the optimal system in the linear-quadratic regulator problem. It is based on the results of the algebraic Riccati equation (ARE) which establish the invariance of certain eigenspaces of the associated Hamiltonian matrix with respect to certain perturbations of Q and the degree of relative stability.<
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