Most real physical systems are nonlinear in nature. Control and ?ltering
of nonlinear systems are still open problems due to their complexity
natures. These problem becomes more complex when the system's parameters
are - certain. A common approach to designing a controller/?lter for an
uncertain nonlinear system is to linearize the system about an operating
point, and uses linear control theory to design a controller/?lter. This
approach is successful when the operating point of the system is
restricted to a certain region. H- ever, when a wide range operation of
the system is required, this method may fail.
ThisbookpresentsnewnovelmethodologiesfordesigningrobustH fuzzy ?
controllers and robustH fuzzy ?lters for a class of uncertain fuzzy
systems ? (UFSs), uncertain fuzzy Markovian jump systems (UFMJSs),
uncertain fuzzy singularly perturbed systems (UFSPSs) and uncertain
fuzzy singularly p- turbed systems with Markovian jumps (UFSPS-MJs).
These new meth- ologies provide a framework for designing robustH fuzzy
controllers and ? robustH fuzzy ?lters for these classes of systems
based on a Tagaki-Sugeno ? (TS) fuzzy model. Solutions to the design
problems are presented in terms of linear matrix inequalities (LMIs). To
investigate the design problems, we ?rst describe a class of uncertain
nonlinear systems (UNSs), uncertain nonlinear
Markovianjumpsystems(UNMJSs), uncertainnonlinearsingularlyperturbed
systems(UNSPSs)anduncertainnonlinearsingularlyperturbedsystemswith
Markovian jumps (UNSPS-MJs) by a TS fuzzy system with parametric -
certainties and with/without Markovian jumps. Then, based on an LMI -
proach, we develop a technique for designing robustH fuzzy controllers
and ? robustH fuzzy ?lters such that a given prescribed performance
index is ? guaranteed.
