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Research Papers

Robust Full-Order and Reduced-Order Observers for a Class of Uncertain Switched Systems

[+] Author and Article Information
Junqi Yang

College of Electrical Engineering
and Automation,
Henan Polytechnic University,
Jiaozuo 454000, China
e-mail: yjq@hpu.edu.cn

Fanglai Zhu

College of Electronics
and Information Engineering,
Tongji University,
Shanghai 201804, China
e-mail: zhufanglai@tongji.edu.cn

Xingguo Tan

College of Electrical Engineering
and Automation,
Henan Polytechnic University,
Jiaozuo 454000, China
e-mail: tanxg@hpu.edu.cn

Yunjian Wang

College of Electrical Engineering
and Automation,
Henan Polytechnic University,
Jiaozuo 454000, China
e-mail: yunjian_wang@163.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 8, 2015; final manuscript received November 12, 2015; published online December 15, 2015. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(2), 021004 (Dec 15, 2015) (9 pages) Paper No: DS-15-1261; doi: 10.1115/1.4032067 History: Received June 08, 2015; Revised November 12, 2015

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system.

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Figures

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Fig. 3

State estimation error curves and switching signal ρ(t) with τa=1.5

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Fig. 4

State estimation error curves and switching signal ρ(t) with τa=0.5

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Fig. 2

State estimation error curves and switching signal ρ(t) with τa=1

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Fig. 5

Estimation for state χ2

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Fig. 6

Estimation for state x2

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