H∞ Filtering for a class of nonlinear switched systems with stable and unstable subsystems

This paper studies the H∞ filtering problem for a class of nonlinear switched systems with stable and unstable subsystems. The Takagi-Sugeno (T-S) fuzzy model is used to approximate each nonlinear subsystem. Using the T-S fuzzy model, the nonlinear switched systems are modeled into the switched T-S fuzzy systems. To guarantee the designed filters can correctly estimate the output of switched systems with unstable subsystems, a set of mode-dependent filters of a Luenberger-like observer type is constructed. In contrast to the filtering error system constructed by the augmentation technique, the filtering error system considered in our work does not contain any unstable filtering error subsystems even with the existence of unstable subsystems in switched systems. The multiple Lyapunov functions approach and the mode-dependent average dwell time technique are employed to solve the H∞ filtering problem. New sufficient conditions for the existence of H∞ filters for the switched T-S fuzzy systems with unstable subsystems are developed. The obtained results can ensure the filtering error system to be asymptotically stable with a prescribed H∞ performance index and have less computational burden. Moreover, the desired H∞ filters can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given.