I am working with an Arduino and a real time clock chip. The chip compensates for leap years and such, so it will always have the correct date, but it does not handle daylight s
While it is easy to calculate whether a particular date is in DST for a particular location under the current rules, do note that DST is at the whim of politicians and could change at any point. I have a clock manufactured pre-2007 that automatically adjusts for daylight savings time, and now I have to change it four times a year: twice when the actual change occurs, and twice when it now-incorrectly changes itself at the old dates.
In this case, you might be able to ignore DST completely by the simple expedient of having the user enter the timezone along with the date and time. Or you could do like most consumer devices and let the user adjust the time to the local time zone twice a year.
But if you really need to handle DST and really want to do things right, use the zoneinfo database and make sure it can be updated somehow. If you can't do that for some reason, at least allow the user to override the rules. And if even that is too difficult, at least give the user the option to turn off automatic adjustments (unlike my stupid alarm clock).