Contribution to the state observation and nonlinear filtering of Takagi-Sugeno models

Abstract

The objective of this thesis is to develop methods for designing observers and H∞ filters for continuous-time switche nonlinear systems with Takagi–Sugeno(T-S) fuzzy models representing the nonlinear system in each mode.These estimation techniques are investigated under state-dependent switching laws(dwell-time-independent),bounded disturbances, and asynchronous switching,where the observer’s or filter’s active switching mode does not necessarily match that of the switched T-S system. First,switched T-S observers are proposed along with Lipschitz constraints,which allow state estimations when the systems’premise variables are not necessarily measurable.However,due to the conservatism that might arise from the Lipschitz constraint,an interesting approach to dealing with unmeasured premise variables is investigated instead in the second part of this thesis in the context of H∞ filtering.Thus,the switched T-S system is modelled as a switched T-S model with nonlinear consequent parts,in which the unmeasured nonlinearities are kept in the nonlinear consequent parts.Thanks to the incremental quadratic constraint employed to deal with unmeasured nonlinearities,the obtained conditions are less conservative compared to the Lipschitz constraint.Furthermore, acknowledging that T-S models only represent nonlinear ones on subsets of their state space,an optimization procedure to estimate the filtering error’s domain of attraction is developed.To deal with the asynchronous switching modes,multiple Lyapunov function candidates are considered,along with a H∞ criterion to minimize the transfer between the input/ output disturbances and state estimation/filtering errors. Moreover,the proposed design conditions are formulated in terms of Linear Matrix Inequalities (LMI).Several illustrative examples are used throughout the manuscript to validate the proposed observers and filters,as well as the obtained results.