$H_\infty$ Filtering of Fuzzy Impulsive Switched Systems With Multipath Quantizations and Packet Dropouts via Multiple Hybrid Strategies

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.