Approximation of the spectral abscissa for switched linear systems via generalized coordinate transformations

For a class of 3rd-order switched linear systems, we explore a way to approximate the spectral abscissa by means of generalized coordinate transformations. Base on the classic result of matrix equation, the minimum of matrix set measure can be obtained after each transformation. By applying transformations iteratively, a computational procedure is developed for finding the transformation matrix and the least μ₁ measure of the equivalence system which can be used as an upper bound estimate of the spectral abscissa.