Minimum phase robustness margin for second-order systems with multidirectional perturbations

The problem of minimum phase robustness for a second-order mass–dashpot–spring system is studied. The allowable margin for multidirectional perturbations of the input and output influence matrices is derived in terms of structured singular value to guarantee minimum phase of the system. Within the margin, the minimum phase property can still be ensured even the actuators and sensors are not collocated. To obtain less conservative results, the perturbation matrix with minimal dimension is derived in the paper. Two examples are used to illustrate the proposed approach.