A finite automaton approximation of the behaviour of first-order stationary continuous plants

For linear first order asymptotically stable plants the source of whose input signals is constrained by many conditions it is shown that a finite deterministic automaton can be designed such that with coordinated initial states of the plant and the automaton the output signals of the latter can at any specified discrete times (of any frequency) differ from the associated output signals of the plant generated in response to all feasible input signals by no more than a specified (as small as desired but non-zero) value.