From 1390 to 1471, France and England took turns having mad rulers, Charles VI for France, and Henry VI for England. In both cases, regents took over- just as would happen if the king were a child. But of course a juvenile king would eventually grow to take power, while an insane king could live for quite some time, and might have spells of lucidity during which he tried to assert his authority. In both France and England, the long power vacuum created by the King being unstable or not capable allowed disputes among the regents and opened the way for other claimants to the throne. Without the regent brother and cousin of Charles VI being at odds, it's quite likely Henry V would not have been successful in his invasion of France. And if Henry VI had been capable, the Wars of the Roses would likely never have started, or at least run for so long.

The monarch who fits your description to a tee is George III of England, who ruled from 1760-1820.

The following information comes from my professor and Paul Monod's "Imperial Island."

Basically, after Pitt's resignation from the government in 1801, George descends into almost full insanity due to an endocrinological disease, porphyria. He did have times of lucidity, but that lasted until 1810. Afterwards, his son, who became George IV, served as Prince Regent and handled his father's matters until George III's death in 1820. In fact, from 1810-1820, he was "treated with opium and straitjackets. He went blind and senile." The British public never found out the full extent of his illness.

George's illness beginning in 1789 actually set off a "Regency Crisis" as it became a point of debate between Charles James Fox and Pitt over whether an Act of Parliament was necessary to place George IV on the thrones as Regent. Pitt claimed that "the Prince of Wales had no more claim to hold the executive government of this country than any other subject whatsoever" and wanted to limit the Regent's power. Basically though, no one thought the Prince should be on thrones without Parliament's approval, and wanted to use the opportunity to further limit the sovereign's power.

Meanwhile, Monod describes the public as very loyal and loving towards George III, viewing him as a faithful husband and good father to his children. This idealized version of George was incorrect, as he did not have a good relationship with many of his children.

This period of English history is incredibly interesting, because an increasingly ill George still viewed himself as a figure of political importance, whereas the government ministers and even the people viewed him more as a figurehead than a politically important figure.

I can provide one historical instance from ottoman empire.

Ibrahim the mad (5 November 1615 – 18 August 1648) rose to power, well actually forced into power in 1640. He was held as semi-prisoner from the day he was born due to the 'kafes' system which means ''cage'' in turkish. ( ottoman tradition after 17th century )

When his older brother Murad IV rose to power ( during a very chaotic phase of the empire ), he executed all his brothers except Ibrahim, which ade him paranoid, terrorized and psychotic.

When murad died, Grand vizier and Ibrahim's mother ( also Murad's mother ) informed him that his brother is dead and, since he is the only male heir left, he must rule. He freaked out and thought it was a trap by Murad to test his loyalty. Later when he saw and touched the remains, he gave in.

He was mad without question. Both foreign ambassadors and turkish records of time are sure about that part. But he did a good job actually until he didn't ( except feeding fish with gold was his daily routine )

He reformed coinage system, frequently disguised himself as a commoner and inspected the city, made peace with austria. Which was usually perceived favorably. Rhodoes knights were attacking ottoman trade ships and using crete as a safe haven. He ordered the invasion of the island, thus starting a 24 year old war with venetians. Invasion was successful, although a small part held on while the things on the naval front was failure. Venetians blockaded dardanalles. Heavy taxes, and good shortage due to blockade caused a revolt led by janissaries and blessed by religious scholars. Mob strangled him and tore him to thousand pieces with their hands.

He suffered from extreme headaches, delusions, paranoia and pretty quite harmless habit of feeding fish with gold.