Not exactly, they do not have complete control. States can choose their timezone, they can choose whether to adopt DST or not. They cannot choose to switch to DST all year round though.

Edit:

http://timezonereport.com/?page_id=313

The bottom line here is that a state (or other political subdivision — see the Wayne County, KY reference below) can only:

- Opt out of DST

- If not opted out of DST, you must advance an hour starting on the second Sunday of March and ending on the first Sunday in November.

- Petition the Secretary of the Department of Transportation and request a change of time zone designation.