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Optimal guaranteed cost control of discrete-time uncertain linear systems. (English) Zbl 0911.93048

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.

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

Citations:

Zbl 0817.93025
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