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 g raduate students interested in systems analysis and design, and is a welcome addition to the literature for researchers and practitioners in these areas.