Q:

How to use "due to" for two clauses

I am wondering which of the following sentences is properly written:

This is due to {First Clause} and to {Second Clause}.

or

This is due to {First Clause} and {Second Clause}.

The question is how we should distribute "to" between clauses? This question also remains for other phrases which have "to" at the end of. 

A:

There's nothing syntactically wrong with due to X and Y; but in any given context it may be desirable to repeat either to or due to to avoid ambiguity and keep your structure apparent to your readers.
Generally, you will want to repeat one or both of these if X is 'heavy': very long or very complex. When you've taken your readers down a long path in one direction and then suddenly return to the head of the path and start off in a different direction, you want to carry them with you to the point where the two paths diverge. 
And in some instances you need to make clear that you're not still on the first path.  Look at your example:

This is due to the abundance of controller and observer design techniques available for ODEs and also mathematical complexities of dealing with an infinite dimensional space

As it stands, many readers will assume at first glance that and also mathematical complexities is conjoined with ODEs, that ODEs and complexities are two classes of things for which techniques are available.
And inserting to before mathematical complexities merely pushes the misunderstanding back a step and leaves them wondering why techniques are available for ODEs but available to mathematical complexities. 
Acute readers, of course, will eventually figure out what you mean. But they  will be at least a little annoyed and impatient; and your incoherence may lead them to doubt your intellectual acumen.
Your job as a writer is to make it as easy as possible for your readers to understand what you mean—to assure that they do not misunderstand, to hold their rapt attention, and not least as a courtesy you owe them for condescending to spend their valuable time on your work.
At the very least you need to repeat both due and to: 

This is due to the abundance of controller and observer design techniques available for ODEs, and due also to the mathematical complexities of dealing with an infinite dimensional space.

Me, I'd be even more explicit:  

This is due on the one hand to the abundance of controller and observer design techniques available for ODEs, and on the other to the mathematical complexities of dealing with an infinite dimensional space.  

It's eight words longer, to be sure; but the microseconds it takes to read the two fixed phrases on the one hand and on the other is I think more than offset by the reduced parsing time required.

