An algorithm of uniform ultimate boundedness for switched linear systems

Uniform ultimate boundedness of a new class of switched linear systems is considered. A switched linear system in this class consists of m subsystems, and none of the individual subsystems need to be stabilizable. The switched linear system is shown to be uniformly ultimately bounded for any pre-given bound if the combination of controllable components of states for all subsystems covers the entire state space. An algorithm for the design of continuous controllers and the switching strategy is given to provide the design of continuous controllers and the switching strategy. Finally, the simulations show the validity of the result.