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The multiple hybrid strategies are developed in this article to investigate the $H_\infty$ filtering problem of fuzzy impulse switched systems (ISSs) with multipath quantizations and packet dropouts. Every subsystem of the fuzzy ISSs is represented by the Takagi–Sugeno fuzzy model. “Multipath quantizations and packet dropouts” mean that both quantizations and packet dropouts exist in the measurable outputs and performance outputs simultaneously. The static quantization strategy is adopted. The packet dropouts are modeled as two random sequences, which are mutually independent and obey the Bernoulli distribution. The multiple hybrid strategies have the following two aspects. First, the filter state update laws are designed besides designing the switching filters for every subsystem, which are specially designed for the impulsive behaviors existing in the ISSs. Second, the mode dependent and mode independent hybrid filters are designed since the filters may not always access the mode switching information of ISSs owing to the quantizations and packet dropouts. Combining the average dwell-time approach and multiple Lyapunov functions, sufficient conditions based on linear matrix inequalities are derived to design the multiple hybrid $H_\infty$ filters. Based on the designed filters, the filtering error systems are exponentially mean-square stable and achieve a weighted $H_\infty$ performance index. Lastly, a practical example is given.

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.

This article investigates the asynchronous nonfragile mixed $H_\infty$ and $L_{2}-L_\infty$ dynamical output feedback (DOF) control problem for switched Takagi–Sugeno (T–S) fuzzy systems with multiple state impulsive jumps. The novelties lie in the following three aspects. First, the novel mixed $H_\infty$ and $L_{2}-L_\infty$ performance index is adopted, which can include the $H_\infty$ performance and $L_{2}-L_\infty$ performance indices as special cases. Second, besides the switching DOF control law for every subsystem, an additional controller state jump rule is employed at controller switching instant. Third, the “multiple state impulsive jumps” means that not only the system states, but also the controller states will jump, and these two different types of switching perform asynchronously. The average dwell time approach is used to design the switching law. By employing a new type of Lyapunov-like functions permitting to increase during the asynchronous period and jump at system switching and controller switching instants, new criteria are established to guarantee the asymptotical stability with a mixed $H_\infty$ and $L_{2}-L_\infty$ performance index of the switched T–S fuzzy systems with multiple state impulsive jumps and asynchronous switching. Then, controller design conditions are obtained in the form of linear matrix inequalities. Finally, two examples are provided to illustrate the effectiveness of the derived results.