What defines the influence of your leader?

I know that breaking alliances costs influence, but does keeping alliances or being otherwise trustworthy raise influence.

Successful crusades increase influence, but I'm playing VI.

Finally, is it a 'personal' thing, defined by command rating, acumen etc? If it is, surely influence will be on an ever-decreasing spiral? One average king begetting a below-average king with low influence, begetting a worse king with worse influence... Bang! Civil War.

Any advice?