On the sensitivity of a time-optimal switching function

The feedback control which achieves minimum-time transition to the state origin for nonoscillatory second-order plants with scalar saturable input involves a function of state raised to a power α which corresponds to the ratio of the plant eigenvalues. The feedback system is found to be acutely sensitive to variations in the parameter α, viz., the state origin cannot be reached in finite time under arbitrarily small α-perturbations.