Controller Design for Linear Time-Periodic Delay Systems via A Symbolic Approach

Haitao Ma, Venkatesh Deshmukh, Eric Butcher, Victoria Averina

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

4 Citations (Scopus)

Abstract

This paper presents a symbolic method for the delayed state feedback controller (DSFC) design for the linear time-periodic delay (LTPD) systems that are open loop unstable. By using shifted Chebyshev polynomials, the closed loop "monodromy matrix" of the LTPD system is obtained symbolically in terms of controller parameters. The stability criterion is given in terms of the eigenvalues of such a symbolic monodromy matrix. This enables one to design a delayed state feedback controller (DSFC) to asymptotically stabilize the original unstable dynamic system. Two controllers designs are presented. The first design is a constant gain DSFC and the second one is a periodic gain DSFC. The periodic gain DSFC has a larger region of stability in the parameter space than the constant gain DSFC. The asymptotic stability of the LTPD system obtained by the proposed method is illustrated in numerical examples by stabilizing an open loop unstable delayed Mathieu equation.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
Pages2126-2131
Number of pages6
Volume3
StatePublished - 2003
Externally publishedYes
Event2003 American Control Conference - Denver, CO, United States
Duration: Jun 4 2003Jun 6 2003

Other

Other2003 American Control Conference
CountryUnited States
CityDenver, CO
Period6/4/036/6/03

Fingerprint

State feedback
Controllers
Stability criteria
Asymptotic stability
Dynamical systems
Polynomials

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Ma, H., Deshmukh, V., Butcher, E., & Averina, V. (2003). Controller Design for Linear Time-Periodic Delay Systems via A Symbolic Approach. In Proceedings of the American Control Conference (Vol. 3, pp. 2126-2131)

Controller Design for Linear Time-Periodic Delay Systems via A Symbolic Approach. / Ma, Haitao; Deshmukh, Venkatesh; Butcher, Eric; Averina, Victoria.

Proceedings of the American Control Conference. Vol. 3 2003. p. 2126-2131.

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

Ma, H, Deshmukh, V, Butcher, E & Averina, V 2003, Controller Design for Linear Time-Periodic Delay Systems via A Symbolic Approach. in Proceedings of the American Control Conference. vol. 3, pp. 2126-2131, 2003 American Control Conference, Denver, CO, United States, 6/4/03.
Ma H, Deshmukh V, Butcher E, Averina V. Controller Design for Linear Time-Periodic Delay Systems via A Symbolic Approach. In Proceedings of the American Control Conference. Vol. 3. 2003. p. 2126-2131
Ma, Haitao ; Deshmukh, Venkatesh ; Butcher, Eric ; Averina, Victoria. / Controller Design for Linear Time-Periodic Delay Systems via A Symbolic Approach. Proceedings of the American Control Conference. Vol. 3 2003. pp. 2126-2131
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