On the prescribed-time attractivity and frozen-time eigenvalues of linear time-varying systems

A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the attractivity of linear time-varying (LTV) systems. It proved that frozen-time eigenvalues a LTV have negative real parts when time sufficiently close to convergence moment. This result shows ubiquitous singularity problem systems can be avoided without instability effects by switching corresponding appropriate Consequently, it state-feedback gain controller, designed unknown time-invariant system, approaches set stabilizing constant gains.