On robust stability of switched linear systems

In this study, the robust stability of continuous‐time switched linear systems is investigated under the assumptions that the matrices of the associated linear subsystems are subjected to affine perturbations. The notion of structured stability radius of a switched linear system which is asymptotically exponentially stable w.r.t. arbitrary switchings is introduced. Some lower bounds and upper bounds for estimating this radius are established, by using the system's common quadratic Lyapunov functions and via an approach based on solutions comparison principle. When the nominal switched system is of special structures (for instance when all matrices of subsystems are normal) the obtained bounds yield easily computable formulas for calculating or estimating the system's stability radius. Several examples are provided to illustrate the authors' approach.