A necessary and sufficient stability criterion for linear time-varying systems

In this paper a necessary and sufficient exponential stability criterion is presented for linear time-varying (LTV) systems based on a previously developed parallel D-spectrum concept. This new result is a corrected version of some previously published results, where an important condition has been overlooked. Extensions of the new result to the assessment of exponential stability using a series D-spectrum, and the assessment of asymptotic stability using a relative-mean concept for the PD- and SD-eigenvalues are also discussed.