Controller performance assessment for multivariate switched systems: A tensor-product representation approach

This paper presents the tensor-product representation approach of multivariate switched linear systems for controller performance assessment, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. And, the stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched system admits a stable tensor-product representation of finite dimension. Moreover, the switched control performance analysis is performed on the projectors, the result of which is used to represent the performance of multivariate switched control systems. Finally, a numerical example is to verify the effectiveness of the proposed approach.