Asynchronous Resilent State Estimation of Switched Fuzzy Systems With Multiple State Impulsive Jumps

This work researches the resilent mixed
$H_{\infty }$
and energy-to-peak filter design problem of switched Takagi–Sugeno (T–S) fuzzy systems with asynchronous switching and multiple state impulsive jumps. The novelties include three points. First, a novel mixed
$H_{\infty }$
and energy-to-peak performance index is proposed, which covers the
$H_{\infty }$
performance index and energy-to-peak performance index as special cases. Second, in addition to designing the switching filters, the filter state jump rules are constructed at filter switching instants. Finally, both system states and filter states jump in a asynchronous manner. The switching law is devised through the mode-dependent average dwell time (MDADT) approach. A new type of Lyapunov-like functionals is constructed, which will increase when the subsystem is running with its mismatched filter and jump while the subsystem or the filter is switching. Then, new conditions are deduced to ensure the filtering error systems with multiple state impulsive jumps to be asymptotically stable with a mixed
$H_{\infty }$
and energy-to-peak performance level. Filter design conditions expressing as linear matrix inequality (LMI) are obtained. Finally, the effectiveness of the derived results is illustrated by two examples.