Quadratic Stability of Discrete-Time Switched Systems

Quadratic stability of switched systems consisting of a class of m-discrete subsystems is studied. An interval matrix is constructed to transform the discrete-time switched system into interval system. Then, a sufficient condition is presented in terms of linear matrix inequality for the quadratic stability of discrete-time switched systems under arbitrary switching laws. This condition is much simpler than the other methods because it needs only one linear matrix inequality to solve. A numerical example illustrates the effectiveness of the method.