Stability analysis of unified chaotic systems via switching control

The problem on the existence of a common quadratic Lyapunov function for switched unified chaotic systems is investigated in this paper. Switched unified chaotic systems with a varying parameter are constructed. A sufficient condition on the existence of a common quadratic Lyapunov function is derived in view of the solution to a group of matrix inequalities. By designing linear state feedback controllers, the controlled switched unified chaotic systems can be asymptotically stable via arbitrary switching. Finally, a random numerical example and its simulations illustrate the effectiveness of the switching control approach.