Simultaneous Stabilization Study Of Generalized System

In the paper, Stable factorization theory and State-space realization have been used to analyze the simultaneous stabilization problem of generalized system. A parameterization in term of a stable inverse system and a stable annihilator system has been proposed for all simultaneously stabilizing controllers. Several examples have been used to illustrate simultaneous stabilization using controller. In the paper, we also present algorithms for the solution of simultaneous and strong simultaneous stabilization problem.The central idea behind stable factorization theory is the notion that any rational function (stable or unstable) can be expressed as the ration of two stable coprime rational function. Stable factorization theory is an effect method in study the many variables control system, especially the Bezout identity play an important role in parameterization of controller. In the paper how to use the Stable factorization theory has been studied in properly stabilization, properly detectable and regular generalized system. A description and physical significance of Bezout identity have been analyzed to give a parameterization of all controllers. Moreover a new kind of Bezout identity in generalized system has been studied to construct controller based on general observation.The simultaneous stabilization is concerned with the problem of designing a single compensator that stabilizes each plant in a generalized system, which has been used widely in nonlinear stabilization and robust stabilization. The central idea of simultaneous stabilization in generalized system is using the Bezout identity and Bezout identity based on general observation & compensator to gain a controller to stabilize each plant in a generalized system. The pole-placement has also been studied in the paper. The result was satisfying.