Abstract:

The authors  mainly studied the observability of  autonomous discrete control systems and  nonautonomous discrete control systems using
 Brouwer’s fixed point theorem. We found that if  the nonlinear part f  is continuous in x and bounded and moreover r(M)=n, then the autonomous discrete control system is locally observable. If there exists positive integer N, such that matrix M has column full rank, and f(i,x(i)) is continuous
in x for each i∈［h,h+N-2］, i is a positive integer and bounded, then the nonautonomous discrete control system is locally observable in step h.

Key words: nonlinear discrete control system, observability, Brouwer’s fixed point theorem