EXTENSIONS OF MIXED-MU BOUNDS TO MONOTONIC AND ODD MONOTONIC NONLINEARITIES USING ABSOLUTE STABILITY THEORY

In this paper we make explicit connections between classical absolute stability theory and modern mixed-mu analysis and synthesis. Specifica lly, using the parameter-dependent Lyapunov function framework of Hadd ad and Bernstein and the frequency dependent off-axis circle interpret ation of How and Hall, we extend previous work on absolute stability t heory for monotonic and odd monotonic nonlinearities to provide tight approximations for constant real parameter uncertainty. An immediate a pplication of this framework is the generalization and reformulation o f mixed-mu analysis and synthesis in terms of Lyapunov functions and R iccati equations. This observation is exploited to provide robust, red uced-order controller synthesis while avoiding the standard D, N - K i teration and curve-fitting procedures.