Maximal stability robustness against real plant coefficient uncertainty

This paper contains results on the maximal stability robustness of linear discrete-time SISO systems comprising a plant having real coefficient uncertainty connected to an integrating feedback controller. Firstly, closed form upper bounds on the size of minimal destabilizing numerator and denominator uncertainty are given. Secondly, a classification of nominal plants is proposed according to whether either or both of these robustness bounds can be achieved. Characterisation of plants in these classes is given. Thirdly the results of the work presented here are applied to an example from the robust control literature.