Advanced H-infinity Control: Towards Nonsmooth Theory and Applications

This compact monographis focused ondisturbance attenuation in nonsmooth dynamic systems, developing anH_∞ approach in the nonsmooth setting. Similar to the standard nonlinear H_∞ approach, the proposed nonsmooth design guarantees both the internal asymptotic stability of anominal closed-loop system and the dissipativity inequality, which statesthat 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 andis then utilized as a Lyapunov functiontoensurethe 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 onelectromechanical applicationswithnonsmooth 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 g

raduate students interested in systems analysis and design, and is a welcome additionto the literature forresearchers and practitioners in these areas.