Optimality conditions for reduced-order modeling, estimation, and control for discrete-time linear periodic plants

W. M. Haddad, V. Kapila, E. G. Collins

Research output: Contribution to journalArticlepeer-review

Abstract

For linear time-invariant systems it has been shown that the solutions to the optimal reduced-order modeling, estimation, and control problems can be characterized using optimal projection equations, sets of Riccati and Lyapunov equations coupled by terms containing a projection matrix. These equations provide a strong theoretical connection between standard full-order results such as linear-quadratic Gaussian theory and have also proved useful in the comparison of suboptimal reduction methods with optimal reduced-order methods. In addition, the optimal projection equations have been used as the basis for novel homotopy algorithms for reduced-order design. This paper considers linear periodic plants and develops necessary conditions for the reduced-order modeling, estimation, and control problems. It is shown that the optimal reduced-order model, estimator, and compensator is characterized by means of periodically time-varying systems of equations consisting of coupled Lyapunov and Riccati equations.

Original languageEnglish (US)
Pages (from-to)437-460
Number of pages24
JournalJournal of Mathematical Systems, Estimation, and Control
Volume6
Issue number4
StatePublished - 1996

ASJC Scopus subject areas

  • Engineering(all)

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