Fundamental Equivalence between Delay Independent Stabilization and Quadratic Stabilization

The stabilization problem of linear time-varying uncertain delay systems by means of linear constant memoryless state feedback control is investigated here. In the case when uncertain parameters may vary independently in arbitrarily large bounding sets, the locations of uncertain elements in the system parameters play an important role. So far obtained conditions of this problem have been found to have a particular geometric configuration with respect to the permissible locations of uncertain elements. In this paper, such a previously obtained configuration is developed to a basic form of antisymmetric stepwise configuration which is a necessary and sufficient condition for time-varying uncertain systems without delays to be quadratically stabilizable by means of linear constant state feedback control. It is shown that if a given system satisfies such developed conditions then the system is stabilizable via linear constant state feedback control with regardless to the upper bounds of time-varying uncertain parameters and time-varying delays