Robust State Feedback Design for Uncertain Systems Based on Luenberger Observer

doi:10.16183/j.cnki.jsjtu.2022.328

Abstract

Abstract:

This paper proposes a robust state feedback design method based on a new Luenberger observer for uncertain systems with measurement output matrices containing uncertain parameters. First, in view of the problem that it is challenging to measure state variables in practice, an observer is designed through the feedback of the observation state. Considering the situation that the measurement output matrix contains uncertain parameters in the uncertain system, a new Luenberger observer is designed. Then, based on the new Luenberger observer, and combined with the multi-affine representation and the slack variable framework, the convex linear matrix inequality condition related to the Lyapunov function is obtained, and the robust stability analysis based on linear matrix inequalities is conducted for the closed-loop system. Finally, the feasibility of the above condition is tested by an experiment to show the applicability and effectiveness of the proposed method.

Key words: uncertain systems, Luenberger observer, multi-affine representations, robust design, observed-state

CLC Number:

TP13

ZHAO Dongdong, YAN Lei, ZHOU Xingwen, GENG Zongsheng, YAN Shi. Robust State Feedback Design for Uncertain Systems Based on Luenberger Observer[J]. Journal of Shanghai Jiao Tong University, 2024, 58(4): 492-497.

Figures/Tables 2

References 14

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差异(δ₁, δ₂)	加权因子 (β₂, β_p)	转移特性(γ₂, γ_p)	H_∞性能μ_c
(0, 0)	(1, 1)	(1.5×10^-4, 1.5×10^-4)	1.0561
(0.1, 0)	(1, 1)	(0.421 8, 0.397 0)	1.6531
(0, 0.1)	(1, 1)	(0.038 4, 0.038 4)	1.5573
(0.1, 0.1)	(1, 1)	(0.481 9, 0.428 9)	2.3533
(0.2, 0.2)	(10, 1)	(3.845 1, 3.703 4)	13.3457
(0.2, 0.2)	(1, 1)	(3.939 4, 3.515 5)	无可行解
(0.2, 0.2)	(1, 10)	(4.879 7, 3.137 5)	9.6805