Perhaps a more specific example would help. What you seem to describe is simply a matrix that is a function of time. That is simple to do.

Here is a rotation matrix that depends on time:

{{Cos[t], -Sin[t]}, {Sin[t], Cos[t]}}

Thanks to both, actually I was too sketchy: my system would look like this : Apß=Bp, with A and B square matrices, p vector and ß single variable. (A and B are like Leontiev input/output matrices) Left term is at the beginning of first cycle, right one at the end. The elements of A are given at the beginning, the ones in B are calculated from those in A (following some rules and conditions). p is supposed to be a unique solution, together with ß, that satisfies all preconditions. On second cycle A changes (using the values of B..), so will as a consequence p ( ß too should). And so on..

So we don't have explicit dependance on a continuos time, but a sequence of matrices (A(t) , with t discrete). I couldn't find out how to write this process.