The present thesis employs fuzzy-polynomial control techniques in order to
improve the stability analysis and control of nonlinear systems. Initially, it
reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems,
such as the more relevant results about polynomial and fuzzy polynomial
systems. The basic framework uses fuzzy polynomial models by Taylor series
and sum-of-squares techniques (semidefinite programming) in order to obtain
stability guarantees.
The contributions of the thesis are:
¿ Improved domain of attraction estimation of nonlinear systems for both
continuous-time and discrete-time cases. An iterative methodology based
on invariant-set results is presented for obtaining polynomial boundaries
of such domain of attraction.
¿ Extension of the above problem to the case with bounded persistent disturbances
acting. Different characterizations of inescapable sets with
polynomial boundaries are determined.
¿ State estimation: extension of the previous results in literature to the
case of fuzzy observers with polynomial gains, guaranteeing stability of
the estimation error and inescapability in a subset of the zone where the
model is valid.
¿ Proposal of a polynomial Lyapunov function with discrete delay in order
to improve some polynomial control designs from literature. Preliminary
extension to the fuzzy polynomial case.
Last chapters present a preliminary experimental work in order to check
and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI
