Small Gain, Circle, Positivity, and Popov Analysis of a Maximaum Entropy Controller for a Benchmark Problem

This paper analyses the stability robustness of a Maximum Entropy controller designed for a benchmark problem. Four robustness tests are used: small gain analysis, circle analysis, positive real analysis, and Popov analysis, each of which is guaranteed to give a less conservative result than the previous test. The analysis here is performed graphically although recent research has developed equivalent tests based on Lyapunov theory. The Popov test is seen for this example to yield extremely nonconservative robust stability bounds. The results here illuminate the conservatism of analysis based on traditional small-gain type tests and reveal the importance of analysis tests based on Popov analysis and related parameter-dependent Lyapunov functions.