The commuter air carrier captain's last scheduled flight had terminated in Sacramento on 3/31. He informed his carrier that he would like to be located in the Los Angeles or Santa Barbara area by 4/1. They offered the airplane which needed to be repositioned to Santa Barbara. He had never piloted the airplane solo, but did not want to wait for a co-pilot. The pilot stated he climbed to 17,500 ft, trimmed the airplane for cruise flight, and 'dozed off' several times. When he last awoke the airplane was descending at over 300 kts (VNE is 246 kts). He was only able to recover using electric trim. The upper wing skin panel damage was later observed by a passenger on a subsequent flight. According to the airplane's manufacturer, the airplane would have had to experience a calculated load factor of 7.8 G's to sustain the observed damage to the wing skin panels, stringers and main spars. The pilot stated he had only slept 1-1/2 to 2 hrs during the preceding 24-hr period.