Guaranteed State Estimation for $\mathscr {H}_-/\mathscr {L}_\infty$ Fault Detection of Uncertain Takagi–Sugeno Fuzzy Systems With Unmeasured Nonlinear Consequents

Abstract

We investigate the problem of guaranteed state estimation and robust fault detection of uncertain Takagi–Sugeno (TS) fuzzy systems with unmeasured nonlinearities. The effects of both unknown-but-bounded disturbances and faults are taken into account in the state bounding observer design via zonotopic representation of sets, which aims to reduce set operations to simple matrix calculations. Based on the $P\text{-}$radius criterion, the size of the state bounding observers can be minimized via $\mathscr {L}_\infty$ performance to mitigate the effect of unknown-but-bounded disturbances. Moreover, for fault detection purposes, $\mathscr {H}_-$ performance is taken into account to increase the fault sensibility. The proposed multiobjective $\mathscr {H}_-/\mathscr {L}_\infty$ state bounding observer design is reformulated as an optimization problem under linear matrix inequalities (LMIs). As a result, the tradeoff between robustness with respect to uncertainties and fault sensibility can be effectively achieved using standard solvers for LMI constraints. Numerical experiments and suitable comparative studies are performed with a nonlinear autonomous vehicle system to demonstrate the effectiveness and the practical interests of the proposed state bounding TS fuzzy observer design method.