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Research Papers

# Optimal $H2$ and $H∞$ Mode-Independent Control for Generalized Bernoulli Jump Systems

[+] Author and Article Information
A. R. Fioravanti

Associate Researcher
e-mail: fioravan@dsce.fee.unicamp.br

A. P. C. Gonçalves

Assistant Professor
e-mail: alimped@dsce.fee.unicamp.br

J. C. Geromel

Professor
e-mail: geromel@dsce.fee.unicamp.br
DSCE/FEEC
University of Campinas,
UNICAMP Campinas, SP, Brazil

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 5, 2012; final manuscript received August 9, 2013; published online September 4, 2013. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 136(1), 011004 (Sep 04, 2013) (6 pages) Paper No: DS-12-1173; doi: 10.1115/1.4025240 History: Received June 05, 2012; Revised August 09, 2013

## Abstract

This paper deals with state-feedback control of discrete-time linear jump systems. The random variable representing the system modes has a generalized Bernoulli distribution, which is equivalent to a Markov chain where the transition probability matrix has identical rows. Another assumption is about the availability of the mode to the controller. We derive necessary and sufficient linear matrix inequalities (LMI) conditions to design optimal $H2$ and $H∞$ state-feedback controllers for the particular class of transition probabilities under consideration and subject to partial mode availability constraints or equivalently cluster availability constraints, which include mode-dependent and mode-independent designs as particular cases. All design conditions are expressed in terms of LMIs. The results are illustrated through a numerical example.

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## References

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## Figures

Fig. 3

H2-norm for different waiting periods

Fig. 2

H2-norm ratio for different feedback controllers

Fig. 1

Example: Hanging Crane model

Fig. 4

Monte Carlo average of quadratic cost

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