Stability of discrete control systems

Abstract

Consider the discrete control system
x(t+1) = Ax(t) + Bu(t), y(t) = Hu[t] (*)
for t ∈ T = {0,1,2,...}
We implore the notion of asymptotic controllability to show that, a system which can be stabilized by an arbitrary feedback u+ g(x) an also be stabilized by a linear feedback u+ D(x).

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 547-548