H∞ controller design for Nabla discrete fractional-order systems
Jin-Xi Zhang1, Yuanda Lv2, Xuefeng Zhang2
1State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China.
Abstract:
This article aims to provide several criteria with sufficient conditions for Nabla discrete fractional-order systems to satisfy a certain H∞ performance index. Firstly, the instability region is approximated by a series of union sets of fan-shaped domains, and the mathematical expression of each fan-shaped domain is given. Secondly, by using the above approximation method and the generalized Kalman-Yakubovič-Popov lemma, some criteria with linear matrix inequality (LMI) formulations for the boundedness of the H∞ norm of the transfer function matrix for Nabla discrete FOSs are derived. Thirdly, an LMI-based H∞ state feedback controller design method is provided by using the projection lemma, which is aimed to stabilize the system and optimize its H∞ performance index simultaneously. Finally, the effectiveness of the proposed approach is verified by the accurate numerical solutions and system state responses obtained from two simulation examples.
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