Stabilization of discrete-time switched linear systems based on average passivity

This paper investigates the average passivity, stabilization and stability with finite L₂ gain for discrete-time switched linear systems without direct input/output link. By the method for finding the switching signal to guarantee the passivity of a discrete-time switched linear system with direct input/output link, and combining with the Differential/Difference Representation-DDR method, a u-average output is constructed to preserve the average passivity of the discrete-time switched linear systems without direct input/output link. Then the co-design approach of switching rule and control law is given to stabilize the discrete-time switched linear systems without direct input/output link assumed average passivity. Furthermore, the average passivity is preserved for the average passive discrete-time switched systems with parallel and negative feedback interconnections. A sufficient condition on the stability with finite L₂ gain for the negative feedback interconnected average passive switched systems is also given.