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[size=3]Concise approaches are:[/size] you could use the Tuples function to get the combinations and then, simply, Apply the Plus function:Plus @@@ Tuples[{aa, bb}] Or, as Frank suggested, the outer function with a fourth...
As I understood, you are talking about a Mass on an inclined rough surface. I have used the numerical solve function to get a somhow simplistic...
Another way is as follows [*]The given transfer function  [mcode]discreteClosedLoop = TransferFunctionModel[{{{(3.1886932013146107`*^25+ z (-4.875667541784289*^25+z (-2. 668411863050167*^25+5.395948880048733*^25 z))) ?}}, ...