Introduction -- Convex Hull Representations -- The Maximal Contractively Invariant Ellipsoids.- Composite Quadratic Lyapunov Functions.- Disturbance Tolerance and Rejection.- Partitioning of the Convex Hull.- Control Systems with an Algebraic Loop.- Generalized Piecewise Quadratic Lyapunov Functions.- Linear Systems with Asymmetric Saturation -- Bibliography -- Index.

This monograph investigates the stability and performance of control systems subject to actuator saturation. It presents new results obtained by both improving the treatment of the saturation function and constructing new Lyapunov functions.  In particular, two improved treatments of the saturation function are described that exploit the intricate structural properties of its traditional convex hull representation.  The authors apply these treatments to the estimation of the domain of attraction and the finite-gain L2 performance by using the quadratic Lyapunov function and the composite quadratic Lyapunov function. Additionally, an algebraic computation method is given for the exact determination of the maximal contractively invariant ellipsoid, a level set of a quadratic Lyapunov function. The authors conclude with a look at some of the problems that can be solved by the methods developed and described throughout the book. Numerous step-by-step descriptions, examples, and simulations are provided to illustrate the effectiveness of their results. Stability and Performance of Control Systems with Actuator Saturation will be an invaluable reference for graduate students, researchers, and practitioners in control engineering and applied mathematics.