I'm using a IFX27001TF adjustable voltage regulator from Infineon. Here is a link to the datasheet and the useful schematic is on page 16. I would like to get about 5.3V from the output so I've calculated my resistor values to be R1=100, R2=330. I'm using a 1uF cap on the input and 10uF cap on the output. Instead of giving me a steady 5.3V output, it outputs whatever the supply voltage is minus 1V. I've tried it at voltages up to 10V. I'm using a bench power supply that can output several amps so I don't think that is a problem. I've tried with 1 led at the output, 3 leds at the output, and 3 leds a 3.3V regulator and a arduino Uno board doing stuff. The current draw on that last one was about 100mA so I don't think it's an issue of drawing enough current for it to be stable. Anybody have any idea what is going on or what my next step might be?
Page 17 of the datasheet specifies that the regulator you are using requires at least 100mΩ of output capacitor ESR for stability -- I suspect the control loop is out of whack because the output capacitor ESR is too low. Try sticking a resistor of anywhere between 1Ω and 10Ω in series with the output cap and seeing if that fixes it -- if it does, that indicates the capacitor's the problem. (Note that modern tantalum and polymer electrolytics can have ESR values that are too low to stabilize an older LDO like yours, so it's not purely a ceramic cap problem.)
Of course, you could also try switching to a more modern regulator that doesn't have such annoying requirements on output capacitor ESR.