@bennyboy Do you happen to be familiar with the Routh-Hurwitz Stability Criterion? If so, I have two questions about it:
1) How could a computer implement the special cases of it, when there is a zero in the first column of the matrix? I've implemented the general part of the Hurwitz Criterion in AEC, but I have no idea which method might a computer use to deal with the special cases. Does a computer use limits or does it move to the z-domain? Either way, how?
2) How could we possibly use the Hurwitz Criterion to calculate the range of gain for which a system is stable? The preparation for a laboratory exercise in cybernetics (which I failed a few years ago, so I am attending it again in about a month) is asking us to calculate that range using both the Hurwitz Criterion and the Bode Criterion and to compare the results. But Hurwitz Criterion gives us no ranges, it gives us the number of poles on the right-hand-side of the complex plane (where the real part is positive).
1) How could a computer implement the special cases of it, when there is a zero in the first column of the matrix? I've implemented the general part of the Hurwitz Criterion in AEC, but I have no idea which method might a computer use to deal with the special cases. Does a computer use limits or does it move to the z-domain? Either way, how?
2) How could we possibly use the Hurwitz Criterion to calculate the range of gain for which a system is stable? The preparation for a laboratory exercise in cybernetics (which I failed a few years ago, so I am attending it again in about a month) is asking us to calculate that range using both the Hurwitz Criterion and the Bode Criterion and to compare the results. But Hurwitz Criterion gives us no ranges, it gives us the number of poles on the right-hand-side of the complex plane (where the real part is positive).
