Robust Stability and Game of Hex

摘要

Checking robust stability is in general not an easy task, although Kharitonov's theorem provides a simple criterion for a class of systems. Here, we consider the more general problem of locating the stability boundary in the space of uncertain parameters. Exploiting a concept borrowed from the Hex game, we introduce a simplicial algorithm, which can search and then lock on the approximate crossover region. In this sense, the combinatorial explosion is avoided. Also, some insight into the topological character of the crossover curve is provided.