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Abstract
This paper is concerned with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for Lipschitz nonlinear systems under aperiodically sampled measurements. The developed filter is a hybrid system, whose states undergo a change or reset at sampling instants. The resulting filtering error system is then modelled as a kind of nonlinear impulsive systems. By introducing a time-varying Lyapunov functional candidate, a sufficient condition for the existence of desired filter is derived to ensure the filtering error system asymptotic stability and guarantee an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. The optimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and corresponding filter gain matrix can be obtained by solving a convex problem with linear matrix inequalities (LMIs) constrains. Two examples are given to show the effectiveness of the theoretical results, and our results are less conservative than existing ones through comparisons.
Highlights
As one of essential problems in control and signal processing fields, filtering issue has gotten extensive concern in the past few decades [1]–[3]
Three main methods have been developed for the issues of sampled-data filtering from the modeling technique perspective [32]: discrete-time system approach, impulsive/hybrid system approach and time-delay system approach. 1) discrete-time system approach [28], [31], [33]: Given a fixed data-rate setting, a discrete-time equivalent system is devised, and the theory in the framework of discretetime systems has its place in dealing with the filtering issue of sampled-data systems
One limitation of the discrete-time system method is that the sampling period should be fixed. Another is that discretization loses the information about the inter-sampling behavior [32]. 2) impulsive/hybrid system approach [20], [21], [26]: The main feature of this method is that the impulsive behavior is used to represent the sampling characteristics
Summary
As one of essential problems in control and signal processing fields, filtering (or estimation) issue has gotten extensive concern in the past few decades [1]–[3]. INDEX TERMS Lipschitz nonlinear systems, Sampled-data filtering, H∞ performance, Impulsive system approach.
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