The governor may by proclamation declare the county or city in which troops are serving, or any specific portion thereof, to be under either complete or limited martial law to the extent, in his or her opinion, that the reestablishment or maintenance of law and order may be promoted.

"Complete martial law" is the subordination of all civil authority to the military;

"Limited military law" is a partial subordination of civil authority by the setting up of an additional police power vested in the military force which shall have the right to try all persons apprehended by it in such area by a military tribunal or turn such offender over to civil authorities within five days for further action, during which time the writ of habeas corpus shall be suspended in behalf of such person.