Petersen, Ian R.; McFarlane, Duncan C.; Rotea, Mario A. Optimal guaranteed cost control of discrete-time uncertain linear systems. (English) Zbl 0911.93048 Int. J. Robust Nonlinear Control 8, No. 8, 649-657 (1998). The authors consider the problem of stabilizing linear discrete-time control systems by means of a static state feedback, which minimizes some guaranteed quadratic cost, i.e.the cost under all uncertainties from a given class. Basically, the paper extends results of I. R. Petersen and D. C. McFarlane [IEEE Trans. Autom. Control 39, 1971–1977 (1994; Zbl 0817.93025)] to the discrete time case, but using different techniques. Two main results are presented: The first shows that the existence of a dynamic state feedback implies the existence of a static state feedback with the desired properties. The second result establishes equivalence of the existence of the static state feedback to a suitable LMI. Reviewer: Lars Grüne (Frankfurt) Cited in 31 Documents MSC: 93D99 Stability of control systems 93C55 Discrete-time control/observation systems 15A39 Linear inequalities of matrices 49N10 Linear-quadratic optimal control problems 93D15 Stabilization of systems by feedback Keywords:discrete time system; robust stabilization; quadratic cost; LMI; dynamic state feedback; static state feedback Citations:Zbl 0817.93025 PDFBibTeX XMLCite \textit{I. R. Petersen} et al., Int. J. Robust Nonlinear Control 8, No. 8, 649--657 (1998; Zbl 0911.93048) Full Text: DOI