Robustness of Sampled-data Control Systems with Uncertain Physical Plant Parameters

When a linear plant model is discretized for digital control, then uncertain physical plant parameters enter exponentially into the coefficients of the open and closed-loop characteristic polynomials. The resulting robustness problem can be treated in the same "scaled" parameter space as the corresponding continuous-time problem if the plant is physically modelled by ordinary differential equations. Stability regions for both continuous and sampled systems are studied in their common parameter space. It is shown that the real root boundary at s = 0 for the continuous system is identical to the real root boundary at z = 1 for the sampled system. A new real root boundary at z = -1 arises and the complex root boundary is modified by sampling. The computation of these last two parts of the boundary is reduced to a simpler problem by a rational approximation