Approximating the Spectral Abscissa for Switched Linear Systems via Coordinate Transformations

In this paper, an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems. By applying elementary transformations iteratively, a series of minimums of least μ1 matrix set measures are obtained, which are utilized to approximate the spectral abscissa of the switched system. The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa. Numerical simulations show the effectiveness of the proposed method.