PURPOSE: To improve transient response by setting each initial value of the amount of dynamic state variable of an engine and the integration amount of deviation of revolution according to the engine revolution number in the cases when a throttle is perfectly closed and when idle revolution speed control is started.

CONSTITUTION: An integration operation/gain block 14 calculates the width PA of the driving pulse for controlling the amount of bypath air in idling and ignition timing IT, from the integration amount of the deviation SA between the aimed value Nr of engine revolution speed and an actual value N and the amount of state variable X obtained through estimation of the dynamic internal state of a control subject 12 from the transmission function matrix which is linearly approximated, and controls in idle revolution number N of an engine 12. Each initial value of the amount of variable x and the integration amount of deviation SA in the case when idle revolution speed control is started from coasting is set in accordance with the engine revolution speed in the cases when a throttle is perfectly closed and when control is started, and said initial value of the integration amount of deviation SA is set so that the actual value of revolution is apparently smaller than the aimed value of revolution. Thus, transient response in coasting and in idling can be improved.