On reliability of linear stability robustness analysis

The reliability of linear model-based stability robustness analysis concerning the realistic domain of attraction is examined. Examples are given to show that when there exists any invariant set in the neighborhood of an equilibrium point the linear model-based stability robustness may not be reliable when the domain of attraction accompanying the predicted local stability is taken into account. Bifurcations, as emergences of extraneous invariant sets resulting from variations of parameters over certain critical values, are considered from the viewpoint of latent bifurcations when nonlinearities are included in the working models. It is shown that if the latent bifurcated solution is unstable the stability of the nominal equilibrium solution may not be reliable. This finding is illustrated by simple examples, including those given by P.V. Kokotovic and R. Marino (1986)