On the stabilization of controllable systems

Conditions are obtained for the asymptotic stabilization of linear dynamical systems through the use of linear state-variable feedback. The procedures developed rely on uniform controllability of the given systems, and yield explicit expressions for the transition matrices of the stabilized systems. As a consequence of the treatment, explicit expressions are obtained for Liapunov transformations which reduce the stabilized systems to canonical (phase-variable) form. Results are given for time-varying multivariable (multi-input) systems.