Stability criterions for switched linear systems based on matrix measure

The problem of stability analysis for a class of switched linear systems is studied in this paper based on the theory of matrix measure. The matrix measures of all subsystems are used to determine the stability of the switched linear systems. Based on this, sufficient conditions are reached, which can be used to determine the stability or instability of switched linear systems under arbitrary switching law. If a switching sequence satisfies some conditions, a theorem in this paper can be used to verify if it can stabilize the systems. The obtained conditions are simpler than the reported methods such as multi-Lyapunov functions and hence are easier to check. Numerical examples are used to demonstrate these conditions.