Composite quadratic Lyapunov functions for constrained control systems

By Tingshu Hu, Zongli Lin. Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

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Antiwindup for stable linear systems with input saturation: an LMI-based synthesis (2003, methodology): “The great advantage provided by the LPV framework is that quadratic stability and performance by means of fixed order antiwindup augmentation can be addressed using the LMI-based LPV synthesis ideas in [1] and [3] which derive from a combination of [23] and [8] (see also [12]).”
Dual Matrix Inequalities in Stability and Performance Analysis of Linear Differential/Difference Inclusions (2006, methodology): “The convex hull function was first used for stability purposes in [11, 10] to estimate the domain of attraction for saturated linear systems and systems with a generalized sector condition (where it was called a “composite quadratic” function).”
Saturated control design for linear differential inclusions subject to disturbance (2009, methodology): “The following lemmas are verified in [7, 8].”
Review on computational methods for Lyapunov functions (2015, background): “Hu and Lin 2003 [119] computed so-called composite quadratic Lyapunov functions, whose level sets are the convex hulls of level sets of quadratic Lyapunov functions, for linear systems subject to input saturation and state constraints.”