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.
