Lower bounds for the stability margin of linear discrete systems based on the weighted performance criteria

Lower bounds for the stability margin of linear discrete systems computed from impulse response measurements are presented. These bounds are based on the connection between the weighted performance criteria and the Lyapunov equation. It is shown that positive definite matrices satisfying the Lyapunov equation for a stable system with unknown parameters can be computed from impulse response measurements. The lower bounds for the stability margin can be obtained from the eigenvalues of these matrices. The properties of the method presented are discussed and it is shown that the lower bounds can be improved by increasing the order of the weighting factor.<>