非线性离散控制系统的可观测性

用Brouwer不动点定理研究非线性自治离散控制系统和非自治离散控制系统的可观测性. 结果表明: 当非线性项f关于x连续、 有界, 且r(M)=n时, 自治离散控制系统是局部可观测的; 若存在正整数N使得矩阵M列满秩, 且对每个i∈［h,h+N-2］(i为正整数), f(i,x(i))关于x(i)连续且有界, 则非自治离散控制系统在第h阶段是局部可观测的.

Observability of Nonlinear Discrete Control Systems

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.