Question

Question 7 A digital control system is unstable if any pole is outside the unit circle and/or there are poles of multiplicity greater than one on the unit circle, True False Moving to another question will save this response. MacBook Air

Answer 1

Yes this above statement is true, which is explain in detail in below photo.

Tene Answee A digital control system is unstable if any pole is outside the colt circle oe poles of multiplicity greate e than the one on the unit circle. it me maps decay sentially to be But we consideea explonation- Suppose considee a pole which is inside a unit circle, whose magoitude is less than 1, let us take 2=0.3 to co.3on in the time domain and that function is to going exponen towards zeo. that cause ystem stable. pole which not lies inside unit circle, Let whose magnitude 2=4.. that maps to (4") in the time domain. So Hence the function is going towords in so Hence that cause the system unstable If you have poles with mu with multiplicity is greatee than 1 on the imaginary axis then that also System unstable axis = Unit circle. 1 to exponctionly increases . cause Here imaginary