Applied Mathematics and Optimization

, Volume 61, Issue 2, pp 145–166 | Cite as

On Optimal Feedback Control for Stationary Linear Systems

  • David L. Russell


We study linear-quadratic optimal control problems for finite dimensional stationary linear systems A X+B U=Z with output Y=C X+D U from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.


Stationary system Riccati equations Feedback invertibility 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsVirginia TechBlacksburgUSA

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