Extensions of mixed- mu bounds to monotonic and odd monotonic nonlinearities using absolute stability theory. I

Explicit connections between classical absolute stability theory and modern mixed-μ analysis and synthesis are made. Specifically, using the parameter-dependent Lyapunov function of W. Haddad and D. Bernstein (1991) and the frequency-dependent off-axis circle interpretation of J.P. How and S.R. Hall (1993), the authors extend previous work on absolute stability theory for monotonic and odd monotonic nonlinearities to provide tight approximations for constant real parametric uncertainty. An immediate application of this framework is the generalization and reinterpretation of mixed-μ analysis and synthesis in terms of Lyapunov functions and Riccati equations