On The Simultaneous Stabilization Of Linear Time-varying Systems

The stabilization of a plant has been a hot topic in control theory. Because stabi-lization is a prerequisite for the normal work of the system, so, different scholars study it using their professional knowledge. In this paper, we study stabilization in operator structure of mathematics.Although there are many scholars studying the stabilization of systems who are Mathematician, and showed many equivalent condition of stabilization of systems, and they also studied the simultaneous stabilization of many systems. But this article con-siders the simultaneous stabilization from a new point of view. This paper is based on the Youla parametrization and the generalized Youla parametrization. The generalized Youla parametrization proved that a system is stabilizable if and only if it has one kind of strong representation but not both, and give a parametrization for the stabilizing con-trollers in terms of the given single strong representation. Affected by the generalized Youla parametrization, we put the theorem to the simultaneous stabilization of many systems.In this paper, we give a criterion of simultaneous stabilization of two systems on account of one kind of strong representation and also give a parametrization for all the simultaneous stabilizing controllers. Similarly, we also give a criterion of simultaneous stabilization of many systems and also give a parametrization for all the simultaneous stabilizing controllers. At last, we give an example to show how our results can be ap-plied.