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 language||English (US)|
|Number of pages||24|
|Journal||Journal of Mathematical Systems, Estimation, and Control|
|State||Published - 1996|
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