Simultaneous stabilization via robust stabilization theory

In this paper a new formulation and solution to the general simultaneous stabilization problem (SSP) is given. The new method is based on finding a central plant from a set of plants to be simultaneously stabilized. The theory of robust stabilization can then be applied to the central plant with a bounded perturbation, which encapsulates the plants to be stabilized, in order to solve the SSP. The simultaneous stabilization problem for linear multivariable time-invariant systems has been reformulated as a generalised two-block H^infinity problem in conjunction with robust stabilization.