Control Systems with an Algebraic Loop

Abstract

In Chapter 2, quadratic Lyapunov functions were utilized in the estimation of the domain of attraction for linear systems with saturated linear feedback. Based on different treatments of saturated linear feedback, various conditions were established under which ellipsoids, the level sets of quadratic Lyapunov functions, are contractively invariant and can be used as estimates of the domain of attraction. As generalizations of quadratic Lyapunov functions, Lyapunov functions that are composed from a group of quadratic functions, such as the convex hull Lyapunov function and the max Lyapunov function, were introduced in Chapter 4 and demonstrated to be less conservative than quadratic Lyapunov functions in obtaining estimates of the domain of attraction for linear systems with saturated linear feedback. Such composite quadratic Lyapunov functions were also used in Chapter 5 in the study of the problems of disturbance tolerance and disturbance rejection for linear systems with an algebraic loop and subject to actuator saturation and external disturbances. Note that the Lyapunov functions used in Chapters 2, 4, and 5 do not embody the properties of saturation/deadzone functions.