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Robust Observer Based Control for Stability of Linear Systems: Application to Polytopic Systems

[+] Author and Article Information
Amel Benabdallah

Department of Mathematics,
Faculty of Sciences of Sfax,
Sfax University,
BP 1171, Sfax 3000, Tunisia

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 19, 2012; final manuscript received August 19, 2013; published online September 26, 2013. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 136(1), 014504 (Sep 26, 2013) (6 pages) Paper No: DS-12-1087; doi: 10.1115/1.4025268 History: Received March 19, 2012; Revised August 19, 2013

This paper investigates the problem of global stabilization by output feedback for linear time-invariant systems. We give first a procedure to design a robust observer for the linear system. Then using this robust observer with the robust state feedback control law developed by Molander and Willems (1980, “Synthesis of State Feedback Control Laws With a Specified Gain and Phase Margin,” IEEE Trans. Autom. Control, 25(5), pp. 928–931), we construct an output feedback which yields a closed loop system with robustness characteristics. That is, we establish a separation principle. Finally, we give sufficient conditions to establish a robust output feedback for linear polytopic systems.

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References

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Figures

Grahic Jump Location
Fig. 1

An illustration of the sector condition

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Fig. 2

Exponential convergence of the error between estimate states and real states

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Fig. 3

Exponential convergence of the closed loop with state feedback

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Fig. 4

Exponential convergence of the closed loop system with observer based state feedback

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