Symbolic and Algebraic Computation in Robust Stability Analysis

Nainn-Ping Ke, University of Southern California, Electrical Engineering - Systems

The objective of this talk is to describe a new method in robust stability analysis which the mu problem can be formulated as solving polynomial systems by using singularity theory and symbolic computation. Once the solutions are found, the mu problem can be easily solved. However, for real mu problem, there could be thousands or even millions polynomial systems which need to be solved in order to find all singularities to determine whether the boundary of Horowitz template intercept the origin or not. In addition, there could be thousands or even millions edges which are critical. Due to these reasons, it is hard to find an efficient algorithm of singularity related method for real mu computation. Fortunately, different from real case, no matter how many uncertainties, only one polynomial systems needs to be solved for complex mu computation. In addition, there is no critical edges for complex mu computation. Therefore, we might expect there will be an efficient algorithm of singularity related method to compute complex mu.