Resilient H∞ Observer Design for T-S Fuzzy System: A Flexible Edge Structure

In this paper, the resilient $H_{\infty}$ observer design problem for T-S fuzzy system is considered by flexible edge structure, whose the flexible edge structure mainly embody that the desired observer could bear definite perturbances on its parameter matrices. Different from the current observer design methods, the flexible edge can be calculated, and the calculated edge gain can explicitly characterize the tolerance measure of the resilient observer. A sufficient condition ensuring asymptotic stability and $H_{\infty}$ performance of the observer error system is established by a double variables-based decoupling principle, and the flexible edge and the observer gains can be both achieved. The effectiveness of the proposed design approach is illustrated by two examples.