TY - JOUR

T1 - Optimality conditions for reduced-order modeling, estimation, and control for discrete-time linear periodic plants

AU - Haddad, W. M.

AU - Kapila, V.

AU - Collins, E. G.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:0029725674

SN - 1052-0600

VL - 6

SP - 437

EP - 460

JO - Journal of Mathematical Systems, Estimation, and Control

JF - Journal of Mathematical Systems, Estimation, and Control

IS - 4

ER -