Performance estimation of continuous-time autonomous switched linear systems via square coordinate transformations

Abstract

Continuous-time autonomous switched linear systems are important not only theoretically but also practically in various engineering applications. This paper addresses the problem of performance estimation in such systems by approximating the spectral abscissa. Based on the square coordinate transformation methodology, a computational procedure is proposed to get the least ${\mu }_1$ measure of the equivalent system. A systematic way is first introduced to find the transformation matrix in the sense that the ${\mu }_1$ measure of the equivalent system equals the given desired value if it exists. Then, an iterative algorithm is developed to obtain the sequence of ${\mu }_1$ measures of the equivalent system which is convergent, and its limit can be used for estimating the spectral abscissa of the original switched linear system. At last, numerical examples are given to illustrate the effectiveness of the method, which shows that it does overcome the limitations of the transformation orders to get better estimation of spectral abscissa.