A parameter space robustness test for real and complex uncertainties

This paper presents a parameter space robustness test for real and complex parameter variations. The analysis model is formed by isolating the parameter variations from the nominal plant using the standard ΔM uncertainty analysis model. The expansion of the determinant of the return difference matrix for this model forms a polynomial that is called the variation polynomial. The zeros of this polynomial indicate when the parameter uncertainties destabilize the system. The zeros are computed using optimization techniques. This approach is tested on several missile autopilot analysis problems. For analysis problems with only real parameter uncertainties this approach reproduces the deGaston-Safonov real margin algorithm results (1988). For complex uncertainties e^jφ, the set of the smallest phase uncertainties that can destabilize the system are computed as a function of frequency. These results show that it is possible to develop parameter space based analysis tests for dynamic uncertainties, including the class of problems in which the parameters do not appear linearly-fractionally in the analysis model. The same idea of the variation polynomial may be extended to systems which have both real and complex (mixed) parameter variations. This topic is currently under investigation