Set stability and controllability for switched non-homogeneous linear systems

In this paper we consider some control problems of switched non-homogeneous linear systems. First, the set stability of switched non-homogeneous linear systems is considered. It is proved that as the linear parts have a common quadratic Lyapunov function the set stability is assured. The problem of searching smallest attracting set is then considered. Then we assume the switching law is controllable and investigate the controllability condition within the attracting region. Finally, we consider the aggregation and the control of aggregation of flocking behavior. Particularly, the results obtained are implemented to analyzing and manipulating of a group of mobile robots.