Tensor product methods in stability robustness analysis

One of the methods recently utilized in stability robustness analysis uses various matrix compositions. An overview is presented of this method using a tensor product theoretic perspective. The theory of tensor products is rigorously delineated. It is shown how the tensor product enters into the stability robustness analysis. It is also shown that the key role which is played by the tensor product is that it can be used to reduce a robust stability problem to a singularity problem, which leads to a significant simplification. The applications of this method to the stability robustness of matrices with unstructured uncertainties, one-parameter uncertainties, or double-parameter uncertainties are discussed