A piecewise quadratic induced measure approach for approximating the largest divergence rate of switched linear systems

For continuous-time switched linear systems, the largest divergence rate is an important index that characterizes the worst asymptotic performance through switching. The computation of this rate is known to be notoriously difficult. Recently, it has been proven that the largest divergence rate is equal to the least possible common matrix measure of the subsystem matrix set. In this paper, a piecewise quadratic induced measure approach is introduced to approximate the least measure of switched linear systems, which transforms the approximation issue into a series of bilinear matrix inequalities.