Relaxed Co-Design of Attack Detection and Set-Membership Estimation for T–S Fuzzy Systems Subject to Malicious Attacks

This paper is concerned with the attack detection problem of T–S fuzzy systems with unknown but bounded (UBB) noise subject to malicious attacks via the set-membership estimation and a switching multi-mode high-order free-weighting matrix (SMHFM) method. Initially, the SMHFM is developed to address the so-called conservatism problem caused by the one-order free-weighting matrix (OFM) method. To solve this problem, the homogeneous polynomial technique is employed to introduce groups of free-weighting matrices for different switching modes. As a result, the SMHFM is synchronized with the working modes and possesses a high-order feature. Additionally, a switching multi-mode mechanism is implemented to enable the SMHFM to exhibit multiple modes. Time-variant balanced matrices are introduced for different switching modes to adjust the relevant matrix terms. This adjustment allows for obtaining more relaxed conditions, leading to smaller constraint sets and higher accuracy in state estimation. Furthermore, a zonotope-based set-membership (ZS) attack detection algorithm is introduced for T-S fuzzy systems, which is capable of detecting various types of attacks. By utilizing the proposed SMHFM method for attack detection, the level of conservatism in state estimation can be reduced. Finally, two simulation examples are given and some comparisons are made to validate the effectiveness of the proposed methods.