Systems Analysis and Control

Systems Analysis and ControlMatthew M. PeetArizona State UniversityLecture 10: Routh-Hurwitz Stability CriterionOverviewIn this Lecture, you will learn:The Routh-Hurwitz Stability Criterion: Determine whether a system is stable. An easy way to make sure feedback isn t destabilizing Construct the Routh TableM. PeetLecture 10: Control Systems2 / 28A Stability TestWe know that for a system with Transferfunction G(s) =n(s)d(s)Input-Output Stability implies that all roots ofd(s)are in the Left Half-PlaneIAll have negative real (s)Re(s)CRHPQ uestion:How do we determine if all roots ofd(s)have negative real part?

4 a a 2 a 3 a 1 0 a 3 b 2 = det 4 a a a 3 0 a 3 b 3 = det a 4 0 a 3 0 a 3 The denominator is the rst entry from the previous row. The numerator is the determinant of the entries from the previous two rows: I The rst column I The next column following the coe cient b k = det n a a n 2k a n 1 a n 2k 1 a n 1 I If a coe cient doesn’t exist ...

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