Abstract
In this paper, the \begin{document}$\mathcal{H}_∞$\end{document} filtering problem of switched nonlinear system with linear hyper plane switching surface is investigated. A state projection method is introduced to ensure the stability of error system and guarantee a prescribed disturbance attenuation level in the \begin{document}$\mathcal{H}_∞$\end{document} sense, by designing filter gains for each subsystem via solving a set of LMIs and formulating a state projection relation for filter state at switching instant. It is worthwhile to note that the state projection relation is deduced by both Lyapunov functions and the switching surface, which implies the state projection method is suitable for switched system with linear hyper plane switching surface. Finally, a numerical example is provided to illustrate our theoretic findings in this paper.
Highlights
Switched systems have attracted much research attention in control theory field during recent years
From the condition (2) in Lemma 1, we note that the fact that the value of Lyapunov function decreases at switching instant guarantees the switched system stable
It is observed that the designed filter meets the specified requirements. In this example we see that our approach is less conservative than common Lyapunov function approach when the switching set is defined by linear hyper planes
Summary
Switched systems have attracted much research attention in control theory field during recent years. From the condition (2) in Lemma 1, we note that the fact that the value of Lyapunov function decreases at switching instant guarantees the switched system stable This observation motivates the state projection method in the following results, whose main aim is to find an appropriate state projection relation to ensure the condition (2) be satisfied. We will give stability and disturbance attenuation analysis results for a class of switched systems with state jump at switching instants, which plays a key role in solving the H∞ filtering problem in this paper. The switching set Si,j(x) is determined only by the continuous state x1(t) ∈ Rn. we introduce some vectors and matrices that will be used in the following results. Vi(x) ≤ xT (t)(ATi Pi + PiAi)x(t) + 2αi FiT Pix(t) x(t) and it is easy to verify that
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