Mode-Dependent Filtering for Networked Semi-Markov Jump Systems by an AET-Based Round-Robin Protocol

This article is devoted to the mode-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\mathcal {H}}_{\infty }$</tex-math></inline-formula> filtering problem for a class of networked semi-Markov jump systems subject to multisensor transmission noises. Considering the constraints of limited bandwidth in practical engineering applications, a new data transmission mechanism of adaptive event triggered-based round-robin protocol is proposed, which can simultaneously save communication resources and reduce data conflicts between the sensor network and the remote filter. Meanwhile, to more accurately describe the complexity of the communication network environment, the data transmission mechanism includes transmission noises, mode information of the systems and semi-Markov switching parameters, which can enhance the flexibility of data transmission. Then, by utilizing the vector augmentation method, a novel mode-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\mathcal {H}}_{\infty }$</tex-math></inline-formula> filter structure integrating semi-Markov jump modes and sensor scheduling nodes is constructed, which can improve the estimation performance of the filter. Next, by considering the upper bound of sojourn time for all system modes, a non-monotonic Lyapunov function is constructed to get hold of the conservative results by relaxing the monotonic requirement of sojourn time. Based on the semi-definite programming technique and vector augmentation method, sufficient conditions are acquired that guarantee the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\sigma }$</tex-math></inline-formula>-error mean-square stability of filtering error dynamics with prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\mathcal {H}}_{\infty }$</tex-math></inline-formula> performance, and the desired filter parameters can be calculated by solving some recursive linear matrix inequalities. Ultimately, a numerical example and a practical example of F-404 aircraft engine system are carried out to validate the effectiveness and applicability of the proposed filter design strategy.