Advanced H Control: Towards Nonsmooth Theory and Applications

This compact monograph is focused on disturbance attenuation in nonsmooth dynamic systems, developing an H_∞ approach in the nonsmooth setting. Similar to the standard nonlinear H_∞ approach, the proposed nonsmooth design guarantees both the internal asymptotic stability of a nominal closed-loop system and the dissipativity inequality, which states that the size of an error signal is uniformly bounded with respect to the worst-case size of an external disturbance signal. This guarantee is achieved by constructing an energy or storage function that satisfies the dissipativity inequality and is then utilized as a Lyapunov function to ensure the internal stability requirements.

Advanced H_∞ Control is unique in the literature for its treatment of disturbance attenuation in nonsmooth systems. It synthesizes various tools, including Hamilton–Jacobi–Isaacs partial differential inequalities as well as Linear Matrix Inequalities. Along with the finite-dimensional treatment, the synthesis is extended to infinite-dimensional setting, involving time-delay and distributed parameter systems. To help illustrate this synthesis, the book focuses on electromechanical applications with nonsmooth phenomena caused by dry friction, backlash, and sampled-data measurements. Special attention is devoted to implementation issues.

Requiring familiarity with nonlinear systems theory, this book will be accessible to graduate students interested in systems analysis and design, and is a welcome addition to the literature for researchers and practitioners in these areas.

Table of Contents

Part I Introduction
Chapter 1 Linear H∞ Control of Autonomous Systems
Chapter 2 The LMI Approach in an Infinite-Dimensional Setting
Chapter 3 Linear H∞ Control of Time-Varying Systems
Chapter 4 Nonlinear H∞ Control

Part II Nonsmooth H∞ Control
Chapter 5 Elements of Nonsmooth Analysis
Chapter 6 Synthesis of Nonsmooth Systems
Chapter 7 LMI-Based H∞-Boundary Control of Nonsmooth Parabolic and Hyperbolic Systems

Part III Benchmark Applications
Chapter 8 Advanced H∞ Synthesis of Fully Actuated Robot Manipulators with Frictional Joints
Chapter 9 Nonsmooth H∞ Synthesis in the Presence of Backlash
Chapter 10 H∞ Generation of Periodic Motion of Mechanical Systems of One Degree of Underactuation
Chapter 11 LMI-Based H∞ Synthesis of the Current Profile in Tokamak Plasmas