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Abstract
This paper deals with the sampled-data fuzzy observer design problem with time-varying gains under the sensor fault consideration. To this end, a nonlinear system with sensor fault is represented by a Takagi-Sugeno fuzzy model with immeasurable premise variables. The sensor fault considered in this paper is assumed to be a time-varying uncertain matrix included in measurements. The observer is designed to consist of gains varying exponentially between two consecutive sampling instants, by which the equilibrium point of the estimation error dynamics is asymptotically exponentially stabilized. In addition, the observer considered in this paper is assumed not to share the same premise variable with a system. Unlike previous studies, this paper proposes a method handling this mismatched premise problem by using an H-infinity criterion. The proposed observer design condition is formulated in terms of linear matrix inequalities, which is relaxed based on a novel fuzzified Lyapunov-Krasovskii functional and a matrix inequality. Finally, two simulation examples are given to validate the effectiveness of the proposed method.
Highlights
For stable control, it is important to obtain the exact information about states of a system
The fuzzy filter approach has been studied in various fuzzy control systems, including time delays [5], interconnected systems [6], uncertain systems [7], The associate editor coordinating the review of this manuscript and approving it for publication was Salman Ahmed
Motivated by the aforementioned analysis, in this paper, we propose a method to design a sampled-data fuzzy observer with time-varying gains for estimating state variables of a nonlinear system under sensor fault consideration
Summary
It is important to obtain the exact information about states of a system. In general, it is not easy to measure the overall state variables of a system, requiring estimating the remaining state variables form given measurements. For this reason, studies on the state estimation have been actively carried out for several decades [1]–[3]. The Takagi–Sugeno (T–S) fuzzy-model-based approach [4] is noteworthy in the state estimation of nonlinear systems because it provides a systematic design procedure. Studies for the state estimation of T–S fuzzy models are mainly based on either the fuzzy filter [5]–[9] or the fuzzy observer [10]–[17] approaches. The fuzzy filter approach has been studied in various fuzzy control systems, including time delays [5], interconnected systems [6], uncertain systems [7], The associate editor coordinating the review of this manuscript and approving it for publication was Salman Ahmed
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