@article{3037823,
    title = "Guaranteed stability margins and singular value properties of the discrete-time linear quadratic optimal regulator",
    author = "Arvanitis, K.G. and Kalogeropoulos, G. and Giotopoulos, S.",
    journal = "IMA Journal of Mathematical Control and Information",
    year = "2001",
    volume = "18",
    number = "3",
    pages = "299-324",
    issn = "0265-0754, 1471-6887",
    doi = "10.1093/imamci/18.3.299",
    keywords = "Discrete time control systems;  Matrix algebra;  Robustness (control systems);  System stability;  Transfer functions, Discrete-time linear quadratic optimal regulator;  Singular value properties;  Stability margins, Linear equations",
    abstract = "Useful singular value properties for the state feedback discrete linear quadratic (LQ) optimal regulator are established. In particular, new lower bounds for the minimum singular value of the regulator's return difference matrix are suggested. On the basis of these bounds, new guaranteed stability margins for such a type of LQ regulator are established. These margins are more relaxed than the guaranteed stability margins proposed in the literature. Furthermore, our investigation provides guaranteed stability margins in cases where known techniques fail. Moreover, it is verified that, in contrast to what happens in the continuous-time case, the singular values of the closed-loop transfer function of the discrete LQ regulator can be, in general, greater than the singular values of the open-loop transfer function. Moreover, in the case of the output-weighted cost function, the singular values of the closed-loop transfer function of the discrete LQ regulator can be, in general, greater than the output-weighting parameter. In this respect, new results relating the singular values of the closed-loop and the open-loop transfer functions of the discrete LQ regulator, are also established."
}