What is meant by the term singularity in the solution?

Question

I am currently simulating a Digital Down Converter with a feedback loop present in it. When the feedback loop is absent it works fine but when the loop is connected it gives the following error.

Trouble solving algebraic loop containing 'tstfft/Embedded MATLAB Function3' at time 6.643282312925169e-005. Stopping simulation. There may be a singularity in the solution. If the model is correct, try reducing the step size (either by reducing the fixed step size or by tightening the error tolerances).

I have reduced the step size but it's not working.

Here the time at which the error occurs is the sampling time of the filter used.

Please help me understand the term singularity and how to remove it.

Thanks in advance

Answer 1

In general a mathematical singularity is any point where a function or mathematical object is not defined or well behaved. Any point where a function is not differentiable or any point where it diverges is called a singularity. The function 1/x has a singularity at x=0 because the it blows up to infinity. Asking a computer to preform such an operation usually results in a run time error causing the program to terminate.

Answer 2

Singularity is a point at which the derivative does not exist for a given function but every neighborhood of which contains points for which the derivative exists. Also called singular point .