The previous monarch must die or abdicate.
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That the country remains a monarchy.
Monarchs historically came to power because they had the support of the people, the bureaucracy and the aristocracy. Being popular would stop the people from revolting. In Medieval Europe the church provided the clerks for the bureaucracy. Keeping on good terms with the bishops and the Pope would usually ensure the support of the bureaucracy. The aristocracy was usually controlled by handing out prestigious offices. Often the nobles were as rich or richer than the king and had more fighting men. It was important to keep these people loyal. The most important requirement for a new monarch to gain power was for the current monarch to be very unpopular. The most important thing for a reigning monarch to gain more power was to make sure that all important decisions had to be made by him.
For the previous monarch to die, abdicate or "resign their position".
Gain is also taken as Laplace transform of output to Laplace transform of Input . for example voltage gain calculation , it is not necessary to make the energy will be zero in L and C ( if present in the given circuit). But in case of Transfer function to avoid the system dynamics , we have to make the inductor and capacitor energy will be zero as initial condition = 0