Journal of Systems Engineering and Electronics ›› 2009, Vol. 20 ›› Issue (6): 1296-1300.

• CONTROL THEORY AND APPLICATION • Previous Articles     Next Articles

Asymptotic controllability of a class of discrete-time systems with disturbances?

Cai Xiushan, Wang Xiao & Xu Xiuling   

  1. Coll. of Mathematics, Physics and Information Engineering, Zhejiang Normal Univ., Jinhua 321004, P. R. China
  • Online:2009-12-28 Published:2010-01-03

Abstract:

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances. It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function. Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system. In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.