Stability criteria for switched linear systems based on the quadratic forms

The problem of stability analysis for switched linear systems is studied based on the properties of the quadratic form. With the introduction of energy velocity matrix and negative definite space, sufficient conditions for asymptotical stability, instability under arbitrary switching sequence and asymptotical stability under special switching sequence are reached which can be applied to study some types of switched linear systems. These conditions can be applied not only to study the problem of stability analysis for switched linear systems, but also to design the stable switching sequence for a switched linear system. Numerical examples are used to demonstrate the applicability of the proposed methods.