This is hard to answer without knowing the what exactly is going on inside the control loop, which is probably not described with much detail in the datasheet. Saying it is "optimized" for 30 mΩ doesn't say what it really needs or what happens when it's not exactly 30 mΩ. Since they make a issue of the output cap ESR, there should be a min/max ESR spec elsewhere in the datasheet.
Hopefully 0 ESR is OK, else it gets inconvenient. Lower ESR is generally better, and certainly closer to ideal, for a capacitor. Capacitor spec sheets therefore often only spec maximum ESR. In that case you either have to get the guaranteed minimum from the capacitor manufacturer, or add deliberate resistance. A better answer is to stay away from chips that specify a minimum output cap ESR to be stable.
That chip is probably old, as ceramic capacitors have come a long way in the last few years. These have much lower ESR than tantalum, and can now approach such capacitances at reasonable cost. Newer chips now make use of the lower available ESR to get better performance instead of requiring the capacitor to have a high resistance. This is a all around better strategy.
Is it be correct to say that the CSR = ESR + external resistor = 1.3 + 0.5 = 1.8 ohms?
According to a footnote in the datasheet, "CSR(compensation series resistance) refers to the total series resistance, including the equivalent series resistance (ESR) of the capacitor, any series resistance added externally, and PWB trace resistance to CO."
In most cases, the trace resistance will be small enough that you can ignore it, and your formula would be correct enough.
Now I would much rather use a ceramic cap, which from what I've read, has an ESR in the milliohms.
Remember that a ceramic cap in the 10 - 15 uF range is going to be fairly large, which can cause reliability issues (due to mismatched CTE between the cap and board).
It looks like a CSR of 0.1 to 2 ohms would be sufficient.
Notice, comparing figs 28 and 29, that the required CSR changes depending on the capacitor value.
And your capacitor value will change depending on voltage and temperature. But 1-3 Ohms total resistance seems to be okay for any capacitance value.
If I use a ceramic cap instead of the tantalum, and if I add an external resistance of say 1 ohm would this yield proper operation?
Based on the above, this should work. Be sure that your capacitor will have 10 uF or so minimum value over all operating conditions.
Best Answer
In general, the impedance of a capacitor with an ESR can be computed as \begin{equation} \dot{Z}_c = ESR - i\frac{1}{\omega C}.\end{equation} Then, knowing the frequency at which the total impedance is given (f = 100 kHz), just solve the equation for ESR.
Usually, values of ESR higher than 0.1 ohm are considered to be "high", but of course that greatly depends on your application.