ask about control system

Consider a general SISO dynamical system represented by the state equations x(k+1)=f(x(k),u(k),k) y(k)=g(x(k),k) Where x(k)∈R^n, and u(k),y(k)∈R. Further, f and g∈c^1 are any linear or nonlinear functions.what is the mean of state equation and what do this equation in real word ????

[John D'Errico]

But this is your homework. Surely you should make an effort. You will learn by doing. Answers is not here to do your homework though.