Mathematical Tools -- Mathematical Models -- Stability Analysis -- Finite-time Stability of Uncertain Homogeneous and Quasihomogeneous Systems -- Synthesis -- Quasihomogeneous Design -- Unit Feedback Design -- Disturbance Attenuation via Nonsmooth ??-design -- Unit Feedback Control of Infinite-dimensional Systems -- Global Asymptotic Stabilization of Uncertain Linear Systems -- Asymptotic Stabilization of Minimum-phase Semilinear Systems -- Global Asymptotic Stabilization of Uncertain Time-delay Systems -- Electromechanical Applications -- Local Nonsmooth ??-synthesis Under Friction/Backlash Phenomena -- Quasihomogeneous Stabilization of Fully Actuated Systems with Dry Friction -- Hybrid Control of Underactuated Manipulators with Frictional Joints.

A major problem in control engineering is robust feedback design that stabilizes a nominal plant while also attenuating the influence of parameter variations and external disturbances. This monograph addresses this problem in uncertain discontinuous dynamic systems with special attention to electromechanical systems with hard-to-model nonsmooth phenomena such as friction and backlash. Ignoring these phenomena may severely limit performance so the practical utility of existing smooth control algorithms becomes questionable for many electromechanical applications. With this motivation, Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. Although it is primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required; such systems are introduced in the book at the appropriate conceptual level. Being developed for discontinuous systems, the theory is successfully applied to their subclasses – variable-structure and impulsive systems – as well as to finite- and infinite-dimensional systems such as distributed-parameter and time-delay systems. The presentation concentrates on algorithms rather than on technical implementation although theoretical results are illustrated by electromechanical applications. These specific applications complete the book and, together with the introductory theoretical constituents bring some elements of the tutorial to the text.