Can I use a microcontroller to control the output voltage of a switching powersupply?

You can control an LT1377 with a microcontroller but not directly in the manner that you imply.

Agh - system trashed my answer :-( - I'll blame Olin :-)
Again and briefer.

LT1377 datasheet here See circuit diagram below.

(1) PWM output voktage fed back to pin FB.
Place a transistor in series with R2

As PWM duty cycle = switch on time decreases the voltage at FB will decrease and Vout will rise to compensate. PWM output from R1 will need to be filtered and loop response time will increase.

(2) Add external error amp. Feed R1/R2 output to a comparator. Other terminal of comparator = DC derived from PWM from microcontroller. This has the advantage of working at the speed of the comparator and can be as fast as the IC was originally. This is probably the technically best solution at the cost of one comparator section.

(3). Feed voltage from R1/R2 AND filtered PWM output into FB pin. As PWM based DC rises it needs less input from R1/R2 to reach Vref and Vout will drop. This is the lowest cost solution. Control range may be imited.

It is possible, but won't likely result in what you intend. You need the feedback input to receive a representation of the output voltage else the output won't be regulated. If you want to use this chip to do the switching but have the micro control the output voltage, then you need to add a voltage from the micro to the feedback signal, not replace it. With only the micro controlling the feedback signal, the chip will basically slam full on or full off, depending on whether the feedback voltage is above or below the threshold.

The best way would be to have a analog signal derived from the micro (low pass filtered PWM is the easiest) control a current source that dumps additional current onto the feedback node. The more current it dumps, the lower the output voltage. Therefore adjust the resistors to get the highest output voltage you ever want, and additional current will adjust it down from there.

One reason for using a current source is that this won't interfere with the switcher chip's compensation. You could resistor-add another signal, but that changes the dynamics of feedback changes as a function of output changes, which will invalidate compensation assumptions the chip may have been designed for.

A totally different possibility is to lose the switcher chip and do the whole switching power supply control from the micro. I have done that many times. With a sufficiently fast A/D in the micro, you can get quite respectable switching frequencies. Each switching cycle, the micro gets the latest A/D reading, does some math to determine the switch on time for this pulse, adjusts PWM hardware to produce the desired pulse width, starts a new A/D conversion, and does it all again. Lots of embedded power supplies work that way.