On Optimal Feedback Control for Stationary Linear Systems
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.
KeywordsStationary system Riccati equations Feedback invertibility
Unable to display preview. Download preview PDF.
- 2.Halanay, A., Ionescu, V.: Time-Varying Discrete Linear Systems: Input-Output Operators, Riccati Equations, Disturbance Attenuation. Birkhauser, Basel (1994) Google Scholar
- 6.Lasiecka, I., Triggiani, R.: Control Theory for Partial Differential Equations: Continuous and Approximation Theories, vols. I & II. Encyclopedia of Mathematics and Its Applications, vol. 74. Cambridge University Press, Cambridge (2000) Google Scholar
- 10.Sennett, R.E.: Matrix Analysis of Structures. Waveland Press, Long Grove (1994) Google Scholar