H2 state-feedback synthesis for discrete-time systems under positivity constraint

Yoshio Ebihara, Patrizio Colanoli, Jose C. Geromel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper is concerned with the H2 state-feedback synthesis problem for discrete-time systems under positivity constraint on the closed-loop systems. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive semidefinite programs (SDPs) for the computation of the upper bounds of the achievable H2 performance as well as suboptimal gains. However, if we merely rely on the upper bound computation, we cannot draw any definite conclusion on the quality of the computed suboptimal gains. Thus the main issue of the present paper is the lower bound computation, and to this end we derive an SDP for that computation via specific treatment of the finite impulse resonse (FIR) with the idea of time-varying gain synthesis. We show that the lower bounds become tighter as we increase the length of the FIR. By numerical examples we show the soundness of the proposed strategy with upper and lower bounds computation.

Original languageEnglish
Title of host publicationSICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages39-46
Number of pages8
ISBN (Electronic)9784907764586
DOIs
Publication statusPublished - Apr 2 2018
Externally publishedYes
Event2018 SICE International Symposium on Control Systems, SICE ISCS 2018 - Tokyo, Japan
Duration: Mar 9 2018Mar 11 2018

Publication series

NameSICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
Volume2018-January

Other

Other2018 SICE International Symposium on Control Systems, SICE ISCS 2018
CountryJapan
CityTokyo
Period3/9/183/11/18

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All Science Journal Classification (ASJC) codes

  • Process Chemistry and Technology
  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering
  • Control and Optimization

Cite this

Ebihara, Y., Colanoli, P., & Geromel, J. C. (2018). H2 state-feedback synthesis for discrete-time systems under positivity constraint. In SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems (pp. 39-46). (SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/SICEISCS.2018.8330154